Details

analyze502.0ms (4.9%)

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
49.9%	49.9%	0.3%	5
49.9%	49.9%	0.3%	6
49.9%	49.9%	0.3%	7
49.9%	49.9%	0.3%	8
49.9%	49.9%	0.3%	9
49.9%	49.9%	0.3%	10
49.9%	24.9%	25.2%	11
49.9%	24.9%	25.2%	12
49.9%	24.9%	25.2%	13
49.9%	24.9%	25.2%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample2.6s (25.3%)

Symmetry

(sort x y)

Results

1.7s	8255×	body	128	valid
778.0ms	4054×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify318.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

5327×	`fma-def_binary64`
866×	`fma-neg_binary64`
705×	`sub-neg_binary64`
654×	`unsub-neg_binary64`
445×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	35	22
2	101	22
3	269	21
4	805	20
5	2079	20
6	2787	20
7	3848	20
8	4164	20
9	4306	20
10	4090	20
11	4094	20
12	4190	20
13	4488	20
14	4581	20
15	4587	20
16	4587	20
17	4593	20
18	4599	20
19	4599	20
20	4617	20
21	4601	20
22	4601	20
23	9364	20

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))

Compiler

Compiled 120 to 79 computations (34.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log.f64 t))
✓	0.0b	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))
✓	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

series282.0ms (2.8%)

Counts

3 → 128

Calls

3 calls:

249.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
22.0ms	(-.f64 1 (log.f64 t))
11.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
8×	`pow1_binary64`

Counts

3 → 59

Calls

3 calls:

5.0ms	(-.f64 1 (log.f64 t))
0.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
0.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

simplify137.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-neg_binary64`
593×	`exp-sum_binary64`
523×	`fma-def_binary64`
300×	`associate-+l+_binary64`
285×	`sub-neg_binary64`

Counts

187 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	2997
1	318	2754
2	918	2521
3	3268	2521
4	4379	2521
5	5221	2521

prune141.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
	0.2b	(fma.f64 z (+.f64 1 (.f64 (neg.f64 (.f64 (cbrt.f64 (log.f64 t)) (cbrt.f64 (log.f64 t)))) (cbrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
	0.2b	(fma.f64 z (.f64 (.f64 (cbrt.f64 (-.f64 1 (log.f64 t))) (cbrt.f64 (-.f64 1 (log.f64 t)))) (cbrt.f64 (-.f64 1 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 2423 to 1194 computations (50.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 z (log.f64 t)) (.f64 1/2 b))
✓	0.0b	(+.f64 (*.f64 a b) (+.f64 y (+.f64 z x)))
✓	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
✓	0.3b	(*.f64 z (log.f64 t))

series610.0ms (6%)

Counts

4 → 60

Calls

4 calls:

241.0ms	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
233.0ms	(*.f64 z (log.f64 t))
122.0ms	(+.f64 (.f64 z (log.f64 t)) (.f64 1/2 b))
13.0ms	(+.f64 (*.f64 a b) (+.f64 y (+.f64 z x)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-log-exp_binary64`
23×	`sum-log_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

14.0ms	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
7.0ms	(+.f64 (*.f64 a b) (+.f64 y (+.f64 z x)))
4.0ms	(+.f64 (.f64 z (log.f64 t)) (.f64 1/2 b))
3.0ms	(*.f64 z (log.f64 t))

simplify156.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
358×	`cancel-sign-sub-inv_binary64`
221×	`distribute-rgt-neg-in_binary64`
214×	`associate-l_binary64`
192×	`associate-r_binary64`

Counts

167 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	3150
1	659	2997
2	2695	2852
3	4377	2852
4	4998	2852
5	4934	2852

prune216.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	196	8	204

Error

Counts

204 → 8

Alt Table

Status	Error	Program
	30.2b	(fma.f64 (sqrt.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x)))) (sqrt.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x)))) (neg.f64 (fma.f64 z (log.f64 t) (*.f64 1/2 b))))
▶	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.2b	(fma.f64 z (+.f64 1 (.f64 (neg.f64 (.f64 (cbrt.f64 (log.f64 t)) (cbrt.f64 (log.f64 t)))) (cbrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	31.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (log.f64 t))) (.f64 1/2 b)))
	15.8b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (cbrt.f64 (pow.f64 (.f64 z (log.f64 t)) 3)) (*.f64 1/2 b)))
✓	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
	0.2b	(fma.f64 z (.f64 (.f64 (cbrt.f64 (-.f64 1 (log.f64 t))) (cbrt.f64 (-.f64 1 (log.f64 t)))) (cbrt.f64 (-.f64 1 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 6180 to 2071 computations (66.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.3b	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1))
✓	0.5b	(fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)
✓	0.7b	(pow.f64 (log.f64 t) 3)

series1.5s (14.4%)

Counts

4 → 104

Calls

4 calls:

1.2s	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
177.0ms	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1))
51.0ms	(fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)
35.0ms	(pow.f64 (log.f64 t) 3)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
32×	`difference-of-squares_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 115

Calls

4 calls:

10.0ms	(/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1))
2.0ms	(pow.f64 (log.f64 t) 3)
0.0ms	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
0.0ms	(fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)

simplify267.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

660×	`times-frac_binary64`
646×	`fma-def_binary64`
298×	`exp-prod_binary64`
235×	`unswap-sqr_binary64`
209×	`fma-neg_binary64`

Counts

219 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	9641
1	629	8856
2	2034	8650
3	4333	8650
4	4991	8650

prune319.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Error

Counts

202 → 8

Alt Table

Status	Error	Program
	30.2b	(fma.f64 (sqrt.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x)))) (sqrt.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x)))) (neg.f64 (fma.f64 z (log.f64 t) (*.f64 1/2 b))))
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.2b	(fma.f64 z (+.f64 1 (.f64 (neg.f64 (.f64 (cbrt.f64 (log.f64 t)) (cbrt.f64 (log.f64 t)))) (cbrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	31.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (log.f64 t))) (.f64 1/2 b)))
	15.8b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (cbrt.f64 (pow.f64 (.f64 z (log.f64 t)) 3)) (*.f64 1/2 b)))
✓	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
	0.2b	(fma.f64 z (.f64 (.f64 (cbrt.f64 (-.f64 1 (log.f64 t))) (cbrt.f64 (-.f64 1 (log.f64 t)))) (cbrt.f64 (-.f64 1 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 7592 to 4574 computations (39.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 1 (log.f64 t))
✓	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.5b	(cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3))
✓	0.7b	(pow.f64 (-.f64 1 (log.f64 t)) 3)

series305.0ms (3%)

Counts

3 → 92

Calls

3 calls:

258.0ms	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
27.0ms	(pow.f64 (-.f64 1 (log.f64 t)) 3)
20.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`cbrt-prod_binary64`
14×	`cube-prod_binary64`
14×	`unpow-prod-down_binary64`

Counts

3 → 78

Calls

3 calls:

5.0ms	(pow.f64 (-.f64 1 (log.f64 t)) 3)
4.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3))
0.0ms	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

simplify130.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

461×	`associate-l_binary64`
386×	`associate-r_binary64`
381×	`distribute-rgt-in_binary64`
356×	`distribute-lft-in_binary64`
346×	`fma-def_binary64`

Counts

170 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	2876
1	347	2761
2	1057	2581
3	4670	2580
4	5121	2580

prune273.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	158	8	166

Error

Counts

166 → 8

Alt Table

Status	Error	Program
	30.2b	(fma.f64 (sqrt.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x)))) (sqrt.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x)))) (neg.f64 (fma.f64 z (log.f64 t) (*.f64 1/2 b))))
✓	0.1b	(fma.f64 z (/.f64 (-.f64 1 (pow.f64 (log.f64 t) 3)) (fma.f64 (log.f64 t) (+.f64 (log.f64 t) 1) 1)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 z (log.f64 t)) (*.f64 1/2 b)))
	0.1b	(fma.f64 z (/.f64 (-.f64 1 (*.f64 (log.f64 t) (log.f64 t))) (+.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.2b	(fma.f64 z (+.f64 1 (.f64 (neg.f64 (.f64 (cbrt.f64 (log.f64 t)) (cbrt.f64 (log.f64 t)))) (cbrt.f64 (log.f64 t)))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (-.f64 1 (log.f64 t)) 3)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	31.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (log.f64 t))) (.f64 1/2 b)))
	15.8b	(-.f64 (+.f64 (.f64 a b) (+.f64 y (+.f64 z x))) (+.f64 (cbrt.f64 (pow.f64 (.f64 z (log.f64 t)) 3)) (*.f64 1/2 b)))

Compiler

Compiled 3785 to 2075 computations (45.2% saved)

regimes2.1s (20.2%)

Accuracy

Total 0.1b remaining (67.5%)

Threshold costs 0.1b (67.5%)

Counts

105 → 1

Compiler

Compiled 31333 to 21062 computations (32.8% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`e-exp-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	21	21
2	24	21
3	22	21

end288.0ms (2.8%)

Remove: (sort x y)
Compiler: Compiled 306 to 200 computations (34.6% saved)

Details

analyze502.0ms (4.9%)

sample2.6s (25.3%)

simplify318.0ms (3.1%)

prune5.0ms (0%)

localize11.0ms (0.1%)

series282.0ms (2.8%)

rewrite10.0ms (0.1%)

simplify137.0ms (1.3%)

prune141.0ms (1.4%)

localize14.0ms (0.1%)

series610.0ms (6%)

rewrite37.0ms (0.4%)

simplify156.0ms (1.5%)

prune216.0ms (2.1%)

localize21.0ms (0.2%)

series1.5s (14.4%)

rewrite22.0ms (0.2%)

simplify267.0ms (2.6%)

prune319.0ms (3.1%)

localize14.0ms (0.1%)

series305.0ms (3%)

rewrite14.0ms (0.1%)

simplify130.0ms (1.3%)

prune273.0ms (2.7%)

regimes2.1s (20.2%)

simplify5.0ms (0%)

end288.0ms (2.8%)

Profiling