Details

analyze2.3s (27.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample2.9s (33.8%)

Results

1.7s	8256×	body	128	valid
1.1s	5062×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
433×	`exp-sum_binary64`
321×	`distribute-rgt-in_binary64`
303×	`distribute-lft-in_binary64`
279×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	47
1	55	42
2	136	40
3	512	40
4	2106	40
5	4520	40
6	4992	40

prune5.0ms (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

3.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))

Compiler

Compiled 135 to 87 computations (35.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
✓	0.4b	(/.f64 2/3 t)
✓	2.3b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	5.2b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series146.0ms (1.7%)

Counts

4 → 88

Calls

4 calls:

65.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
47.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
32.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2/3 t)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 91

Calls

4 calls:

5.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
5.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
2.0ms	(/.f64 2/3 t)
0.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))

simplify124.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

801×	`times-frac_binary64`
430×	`cancel-sign-sub-inv_binary64`
324×	`fma-neg_binary64`
272×	`sub-neg_binary64`
270×	`fma-def_binary64`

Counts

179 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	321	4150
1	864	3932
2	2992	3925
3	4865	3924
4	4956	3924

prune252.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	186	4	190

Error

0.0b

Counts

190 → 4

Alt Table

Status	Error	Program
▶	9.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (log.f64 (exp.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))))) x))
	31.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
✓	3.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
	20.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))

Compiler

Compiled 7025 to 3559 computations (49.3% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
	0.4b	(/.f64 2/3 t)
✓	3.4b	(log.f64 (exp.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)))
	5.2b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series45.0ms (0.5%)

Counts

1 → 20

Calls

1 calls:

45.0ms

(log.f64 (exp.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`log-pow_binary64`
7×	`exp-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 21

Calls

1 calls:

2.0ms

(log.f64 (exp.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)))

simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

758×	`associate-/l*_binary64`
440×	`times-frac_binary64`
375×	`cancel-sign-sub-inv_binary64`
288×	`fma-neg_binary64`
253×	`associate-r_binary64`

Counts

41 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	789
1	224	743
2	586	739
3	1866	723
4	5476	723

prune227.0ms (2.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	189	4	193

Error

0.0b

Counts

193 → 4

Alt Table

Status	Error	Program
✓	9.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (log.f64 (exp.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))))) x))
	31.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
✓	3.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
▶	20.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))

Compiler

Compiled 7252 to 3588 computations (50.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -5/6 a)
✓	0.0b	(pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a))))
✓	0.2b	(*.f64 b (-.f64 -5/6 a))
✓	1.1b	(fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))

series39.0ms (0.5%)

Counts

4 → 108

Calls

4 calls:

20.0ms	(pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a))))
12.0ms	(fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))
5.0ms	(*.f64 b (-.f64 -5/6 a))
1.0ms	(-.f64 -5/6 a)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
27×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 114

Calls

4 calls:

5.0ms	(*.f64 b (-.f64 -5/6 a))
3.0ms	(-.f64 -5/6 a)
2.0ms	(pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a))))
0.0ms	(fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

491×	`associate-r_binary64`
476×	`cancel-sign-sub-inv_binary64`
409×	`associate-l_binary64`
380×	`unswap-sqr_binary64`
294×	`fma-def_binary64`

Counts

222 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	4240
1	822	3311
2	3355	3218
3	5218	3218

prune271.0ms (3.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	199	4	203

Error

0.0b

Counts

203 → 4

Alt Table

Status	Error	Program
✓	9.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (log.f64 (exp.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))))) x))
▶	31.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
✓	3.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
✓	20.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))

Compiler

Compiled 6475 to 3958 computations (38.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
✓	0.1b	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
✓	0.3b	(*.f64 c -2/3)
✓	1.1b	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)

series84.0ms (1%)

Counts

4 → 123

Calls

4 calls:

47.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)
20.0ms	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
15.0ms	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
1.0ms	(*.f64 c -2/3)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 69

Calls

4 calls:

2.0ms	(*.f64 c -2/3)
2.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)
0.0ms	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
0.0ms	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))

simplify113.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

828×	`times-frac_binary64`
828×	`fma-def_binary64`
276×	`fma-neg_binary64`
259×	`div-sub_binary64`
225×	`distribute-rgt-neg-out_binary64`

Counts

192 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	2934
1	234	2721
2	607	2648
3	1829	2528
4	4577	2528
5	5040	2528

prune142.0ms (1.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	131	4	135

Error

0.0b

Counts

135 → 4

Alt Table

Status	Error	Program
✓	9.7b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (log.f64 (exp.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))))) x))
✓	31.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
✓	3.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
✓	20.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))

Compiler

Compiled 3550 to 1966 computations (44.6% saved)

regimes1.4s (16.8%)

Accuracy

Total 1.4b remaining (94.4%)

Threshold costs 0b (0%)

Counts

96 → 2

Compiler

Compiled 33176 to 24160 computations (27.2% saved)

bsearch4.0ms (0%)

Compiler: Compiled 31 to 23 computations (25.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
17×	`sub-neg_binary64`
15×	`distribute-rgt-neg-in_binary64`
15×	`cancel-sign-sub-inv_binary64`
14×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	111
1	68	111
2	97	111
3	120	111
4	155	111
5	171	111
6	181	111
7	187	111
8	189	111
9	179	111

end120.0ms (1.4%)

Compiler: Compiled 284 to 185 computations (34.9% saved)

Iter	Nodes	Cost
0	49	111
1	68	111
2	97	111
3	120	111
4	155	111
5	171	111
6	181	111
7	187	111
8	189	111
9	179	111

Iter	Nodes	Cost
0	49	111
1	68	111
2	97	111
3	120	111
4	155	111
5	171	111
6	181	111
7	187	111
8	189	111
9	179	111

Details

analyze2.3s (27.2%)

sample2.9s (33.8%)

simplify48.0ms (0.6%)

prune5.0ms (0.1%)

localize19.0ms (0.2%)

series146.0ms (1.7%)

rewrite18.0ms (0.2%)

simplify124.0ms (1.4%)

prune252.0ms (2.9%)

localize25.0ms (0.3%)

series45.0ms (0.5%)

rewrite3.0ms (0%)

simplify52.0ms (0.6%)

prune227.0ms (2.6%)

localize13.0ms (0.2%)

series39.0ms (0.5%)

rewrite19.0ms (0.2%)

simplify99.0ms (1.2%)

prune271.0ms (3.2%)

localize15.0ms (0.2%)

series84.0ms (1%)

rewrite8.0ms (0.1%)

simplify113.0ms (1.3%)

prune142.0ms (1.7%)

regimes1.4s (16.8%)

bsearch4.0ms (0%)

simplify8.0ms (0.1%)

end120.0ms (1.4%)

Profiling

Iter	Nodes	Cost
0	49	111
1	68	111
2	97	111
3	120	111
4	155	111
5	171	111
6	181	111
7	187	111
8	189	111
9	179	111