Details

analyze1.2s (21.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample82.0ms (1.5%)

Algorithm

1×

intervals

Results

43.0ms	125×	body	2048	valid
18.0ms	74×	body	1024	valid
6.0ms	35×	body	512	valid
1.0ms	10×	body	256	valid
1.0ms	12×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

694×	`div-sub_binary64`
602×	`neg-mul-1_binary64`
550×	`sub-neg_binary64`
311×	`associate-/r*_binary64`
286×	`distribute-neg-frac_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	30	21
2	71	21
3	195	21
4	504	21
5	1254	21
6	2437	21
7	3311	21
8	4638	21
9	4955	21

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

0.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.6b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

Compiler

Compiled 30 to 20 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.2b	(.f64 5 (.f64 v v))
0.6b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

rewrite78.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`

Counts

3 → 71

Calls

3 calls:

7.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
4.0ms	(.f64 5 (.f64 v v))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

Compiler

Compiled 1582 to 991 computations (37.4% saved)

series23.0ms (0.4%)

Error

0.6b

Counts

3 → 12

Calls

3 calls:

7.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
7.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
5.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 333 to 284 computations (14.7% saved)

simplify123.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

442×	`associate-l_binary64`
391×	`div-sub_binary64`
376×	`times-frac_binary64`
367×	`associate-r_binary64`
235×	`associate-/l*_binary64`

Counts

83 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1943
1	302	1799
2	973	1785
3	3884	1785
4	4989	1785
5	4926	1785

prune22.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	3	43

Error

0.6b

Counts

43 → 3

Alt Table

Status	Error	Program
▶	0.6b	(acos.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (.f64 v v) 1))))
	0.7b	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))
	1.5b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))

Compiler

Compiled 602 to 406 computations (32.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (*.f64 v v) 1))
0.2b	(.f64 5 (.f64 v v))
0.2b	(.f64 5 (.f64 v v))
0.6b	(acos.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (.f64 v v) 1))))

rewrite110.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

36×	`times-frac_binary64`
36×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
21×	`sqrt-prod_binary64`

Counts

4 → 110

Calls

4 calls:

8.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (*.f64 v v) 1))
4.0ms	(.f64 5 (.f64 v v))
4.0ms	(.f64 5 (.f64 v v))
1.0ms	(acos.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (.f64 v v) 1))))

Compiler

Compiled 3223 to 2106 computations (34.7% saved)

series35.0ms (0.6%)

Error

0.6b

Counts

4 → 15

Calls

4 calls:

8.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (*.f64 v v) 1))
6.0ms	(.f64 5 (.f64 v v))
6.0ms	(.f64 5 (.f64 v v))
5.0ms	(acos.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (.f64 v v) 1))))

Compiler

Compiled 746 to 591 computations (20.8% saved)

simplify137.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

665×	`distribute-rgt-in_binary64`
613×	`div-sub_binary64`
326×	`associate-l_binary64`
261×	`associate-r_binary64`
178×	`times-frac_binary64`

Counts

125 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3021
1	298	2888
2	804	2868
3	2474	2868
4	4655	2868
5	5585	2868

prune43.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	74	3	77

Error

0.6b

Counts

77 → 3

Alt Table

Status	Error	Program
✓	0.6b	(acos.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (.f64 v v) 1))))
▶	0.7b	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))
	1.5b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))

Compiler

Compiled 1335 to 902 computations (32.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (*.f64 v v) (pow.f64 v 4))
0.0b	(.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))
0.6b	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 41

Calls

3 calls:

6.0ms	(.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))
4.0ms	(+.f64 (*.f64 v v) (pow.f64 v 4))
1.0ms	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))

Compiler

Compiled 845 to 563 computations (33.4% saved)

series32.0ms (0.6%)

Error

0.6b

Counts

3 → 15

Calls

3 calls:

11.0ms	(+.f64 (*.f64 v v) (pow.f64 v 4))
10.0ms	(.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))
7.0ms	(acos.f64 (+.f64 -1 (.f64 4 (+.f64 (.f64 v v) (pow.f64 v 4)))))

Compiler

Compiled 369 to 319 computations (13.6% saved)

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

739×	`difference-of-squares_binary64`
512×	`associate-l_binary64`
435×	`associate-r_binary64`
375×	`unswap-sqr_binary64`
197×	`cancel-sign-sub-inv_binary64`

Counts

56 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	957
1	188	842
2	558	836
3	2118	836
4	4012	836
5	6085	836

prune33.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	42	4	46

Error

0.6b

Counts

46 → 4

Alt Table

Status	Error	Program
	2.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))) (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1)))) (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))
▶	0.7b	(exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))
✓	0.6b	(acos.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (.f64 v v) 1))))
	1.5b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))

Compiler

Compiled 798 to 559 computations (29.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1)))
0.0b	(exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))
0.0b	(.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v)))
0.6b	(acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))

rewrite74.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
7×	`add-exp-log_binary64`

Counts

4 → 57

Calls

4 calls:

6.0ms	(.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v)))
2.0ms	(exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))
2.0ms	(acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))
1.0ms	(log.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1)))

Compiler

Compiled 1307 to 943 computations (27.9% saved)

series68.0ms (1.2%)

Error

0.6b

Counts

4 → 15

Calls

4 calls:

23.0ms	(exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))
22.0ms	(log.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1)))
13.0ms	(.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v)))
6.0ms	(acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))

Compiler

Compiled 494 to 437 computations (11.5% saved)

simplify116.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

616×	`distribute-rgt-out_binary64`
485×	`associate-l_binary64`
457×	`distribute-lft-out_binary64`
396×	`associate-r_binary64`
363×	`unswap-sqr_binary64`

Counts

72 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1606
1	189	1376
2	508	1373
3	1810	1361
4	4710	1361
5	4973	1361
6	4980	1361

prune22.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	39	5	44

Error

0.6b

Counts

44 → 5

Alt Table

Status	Error	Program
	2.2b	(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1)) 3))))
	2.6b	(exp.f64 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))) 2)) (log.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))))
	0.7b	(exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 4 (+.f64 (pow.f64 v 4) (.f64 v v))) -1))))
	0.6b	(acos.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 5 (.f64 v v)))) (-.f64 (.f64 v v) 1))))
	1.5b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))) 3))

Compiler

Compiled 562 to 414 computations (26.3% saved)

regimes386.0ms (6.9%)

Accuracy

Total 0.0b remaining (1.8%)

Threshold costs 0.0b (1.8%)

Compiler

Compiled 9677 to 7159 computations (26% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	28	28
2	38	28
3	47	28
4	53	28
5	56	28
6	57	28
7	54	28

end1.0ms (0%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

sample2.8s (49.2%)

Algorithm

1×

intervals

Results

1.6s	3990×	body	2048	valid
515.0ms	1999×	body	1024	valid
179.0ms	983×	body	512	valid
64.0ms	515×	body	256	valid
33.0ms	511×	body	128	valid
1.0ms	2×	body	4096	valid
0.0ms	9×	body	128	nan

Compiler

Compiled 145 to 109 computations (24.8% saved)

Details

analyze1.2s (21.9%)

sample82.0ms (1.5%)

simplify72.0ms (1.3%)

prune1.0ms (0%)

localize7.0ms (0.1%)

rewrite78.0ms (1.4%)

series23.0ms (0.4%)

simplify123.0ms (2.2%)

prune22.0ms (0.4%)

localize11.0ms (0.2%)

rewrite110.0ms (1.9%)

series35.0ms (0.6%)

simplify137.0ms (2.4%)

prune43.0ms (0.8%)

localize9.0ms (0.2%)

rewrite47.0ms (0.8%)

series32.0ms (0.6%)

simplify81.0ms (1.4%)

prune33.0ms (0.6%)

localize11.0ms (0.2%)

rewrite74.0ms (1.3%)

series68.0ms (1.2%)

simplify116.0ms (2.1%)

prune22.0ms (0.4%)

regimes386.0ms (6.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.8s (49.2%)

Profiling