Details

analyze192.0ms (7.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample38.0ms (1.5%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	256	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 45 to 38 computations (15.6% saved)

simplify178.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-def_binary64`
760×	`unsub-neg_binary64`
633×	`distribute-neg-in_binary64`
628×	`distribute-rgt-neg-in_binary64`
564×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	35	19
2	98	17
3	302	15
4	923	7
5	2332	7
6	3226	7
7	3864	7
8	4544	7
9	4793	7
10	4822	7
11	4798	7
12	4830	7
13	4680	7
14	4874	7
15	4821	7

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f64 t (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

Compiler

Compiled 37 to 28 computations (24.3% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 t (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))
✓	0.3b	(*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)

New

Error

Program

✓

0.2b

(*.f64 t (*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

✓

0.3b

(*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 40

Calls

2 calls:

4.0ms

(*.f64 t (*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

3.0ms

(*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)

series16.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

10.0ms

(*.f64 t (*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

6.0ms

(*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)

simplify99.0ms (4%)

Algorithm

1×	egg-herbie

Rules

970×	`fma-def_binary64`
331×	`associate-l_binary64`
261×	`associate-*r/_binary64`
229×	`associate-*l/_binary64`
217×	`*-commutative_binary64`

Counts

64 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	478
1	112	430
2	327	421
3	594	419
4	851	419
5	1427	419
6	3364	419
7	4801	419
8	4930	419

prune43.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Error

0.0b

Counts

109 → 8

Alt Table

Status	Error	Program
▶	0.3b	(.f64 t (.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))
	0.3b	(.f64 (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) t)
	1.3b	(.f64 t (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (.f64 (cbrt.f64 t) 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))
	0.7b	(.f64 t (.f64 (.f64 (sqrt.f64 t) 2028240960365167/10141204801825835211973625643008) (.f64 (sqrt.f64 t) 2028240960365167/10141204801825835211973625643008)))
	0.5b	(.f64 (sqrt.f64 t) (.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064 (pow.f64 t 3/2)))
	0.7b	(.f64 t (cbrt.f64 (pow.f64 (.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064 t) 3)))
	0.5b	(.f64 (sqrt.f64 (.f64 t (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))) (sqrt.f64 (.f64 t (*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))))
	0.7b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)) (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))))

Compiler

Compiled 765 to 495 computations (35.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))
✓	0.2b	(.f64 t (.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))

New

Error

Program

✓

0.2b

(*.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

✓

0.2b

(*.f64 t (*.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 46

Calls

2 calls:

8.0ms

(*.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

6.0ms

(*.f64 t (*.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))

series15.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

9.0ms

(*.f64 t (*.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))

6.0ms

(*.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

simplify73.0ms (3%)

Algorithm

1×	egg-herbie

Rules

649×	`unswap-sqr_binary64`
338×	`associate-+l+_binary64`
276×	`*-commutative_binary64`
268×	`associate-*r/_binary64`
267×	`fma-def_binary64`

Counts

70 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	581
1	154	482
2	528	470
3	797	460
4	1147	460
5	1776	460
6	4885	460

prune50.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	121	8	129

Error

0.0b

Counts

129 → 8

Alt Table

Status	Error	Program
	0.7b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)) (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))))
▶	0.3b	(.f64 (.f64 t (*.f64 t 2028240960365167/10141204801825835211973625643008)) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))
✓	0.3b	(.f64 t (.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))
	0.3b	(.f64 (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) t)
	1.3b	(.f64 t (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (.f64 (cbrt.f64 t) 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))
	0.7b	(.f64 t (.f64 (.f64 (sqrt.f64 t) 2028240960365167/10141204801825835211973625643008) (.f64 (sqrt.f64 t) 2028240960365167/10141204801825835211973625643008)))
	0.5b	(.f64 (sqrt.f64 t) (.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064 (pow.f64 t 3/2)))
	0.6b	(.f64 t (cbrt.f64 (.f64 (pow.f64 t 3) 69617318994479288428505409468106852619915340402670484572597162535910920607533699795135926369/1087770609288739018116276647019455748771006705104961378712461595034426490595025393129804804639189577049885346787832834079429794483512744426310696916513970896780966442670885312576979206144)))

Compiler

Compiled 969 to 718 computations (25.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 t (*.f64 t 2028240960365167/10141204801825835211973625643008)) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))
✓	0.2b	(.f64 t (.f64 t 2028240960365167/10141204801825835211973625643008))

New

Error

Program

✓

0.2b

(*.f64 (*.f64 t (*.f64 t 2028240960365167/10141204801825835211973625643008)) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

✓

0.2b

(*.f64 t (*.f64 t 2028240960365167/10141204801825835211973625643008))

rewrite12.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 46

Calls

2 calls:

6.0ms

(*.f64 (*.f64 t (*.f64 t 2028240960365167/10141204801825835211973625643008)) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

4.0ms

(*.f64 t (*.f64 t 2028240960365167/10141204801825835211973625643008))

series21.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

11.0ms

(*.f64 t (*.f64 t 2028240960365167/10141204801825835211973625643008))

9.0ms

(*.f64 (*.f64 t (*.f64 t 2028240960365167/10141204801825835211973625643008)) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))

simplify69.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

505×	`unswap-sqr_binary64`
326×	`associate-*r/_binary64`
325×	`associate-+l+_binary64`
294×	`associate-*l/_binary64`
271×	`fma-def_binary64`

Counts

70 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	682
1	152	580
2	539	559
3	768	553
4	1067	553
5	1694	553
6	4862	553

prune48.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	135	6	141

Error

Counts

141 → 6

Alt Table

Status	Error	Program
	0.7b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)) (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))))
	0.4b	(.f64 (.f64 2028240960365167/10141204801825835211973625643008 (pow.f64 t 2)) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))
✓	0.3b	(.f64 t (.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))
▶	0.3b	(.f64 (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) t)
	0.4b	(.f64 (.f64 2028240960365167/10141204801825835211973625643008 t) (*.f64 2028240960365167/10141204801825835211973625643008 t))
	0.4b	(expm1.f64 (log1p.f64 (.f64 (.f64 t t) 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))

Compiler

Compiled 946 to 689 computations (27.2% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) t)
	0.3b	(*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)

New

Error

Program

✓

0.2b

(*.f64 (*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) t)

0.3b

(*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 (*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) t)

series10.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(*.f64 (*.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) t)

simplify82.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
420×	`times-frac_binary64`
376×	`distribute-rgt-in_binary64`
318×	`associate-l_binary64`
240×	`sqr-pow_binary64`

Counts

32 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	296
1	89	260
2	281	251
3	551	249
4	761	249
5	1290	249
6	2487	249
7	4441	249
8	4824	249

prune34.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
	0.7b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)) (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))))
	0.4b	(.f64 (.f64 2028240960365167/10141204801825835211973625643008 (pow.f64 t 2)) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064))
✓	0.3b	(.f64 t (.f64 (*.f64 t 2028240960365167/10141204801825835211973625643008) (sqrt.f64 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))
✓	0.3b	(.f64 (.f64 t 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064) t)
	0.4b	(.f64 (.f64 2028240960365167/10141204801825835211973625643008 t) (*.f64 2028240960365167/10141204801825835211973625643008 t))
	0.4b	(expm1.f64 (log1p.f64 (.f64 (.f64 t t) 4113761393303014933413986937889/102844034832575377634685573909834406561420991602098741459288064)))

Compiler

Compiled 642 to 414 computations (35.5% saved)

regimes144.0ms (5.8%)

Accuracy

Total 0.3b remaining (92.4%)

Threshold costs 0.3b (92.4%)

Compiler

Compiled 1876 to 1383 computations (26.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	10	10

end0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample1.3s (52.4%)

Algorithm

1×

intervals

Results

831.0ms	8000×	body	256	valid
126.0ms	8000×	pre	128	true

Compiler

Compiled 92 to 71 computations (22.8% saved)

Details

analyze192.0ms (7.8%)

sample38.0ms (1.5%)

simplify178.0ms (7.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

rewrite7.0ms (0.3%)

series16.0ms (0.6%)

simplify99.0ms (4%)

prune43.0ms (1.7%)

localize5.0ms (0.2%)

rewrite15.0ms (0.6%)

series15.0ms (0.6%)

simplify73.0ms (3%)

prune50.0ms (2%)

localize5.0ms (0.2%)

rewrite12.0ms (0.5%)

series21.0ms (0.8%)

simplify69.0ms (2.8%)

prune48.0ms (1.9%)

localize3.0ms (0.1%)

rewrite5.0ms (0.2%)

series10.0ms (0.4%)

simplify82.0ms (3.3%)

prune34.0ms (1.4%)

regimes144.0ms (5.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (52.4%)

Profiling