Details

analyze1.2s (25.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
25%	74.9%	0.2%	7
25%	74.9%	0.2%	8
34.3%	65.5%	0.2%	9
39%	60.8%	0.2%	10
48.3%	51.5%	0.2%	11
53.7%	46.1%	0.2%	12
63.1%	36.7%	0.2%	13
64%	35.6%	0.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

28×	`cancel-sign-sub-inv_binary64`
21×	`sub-neg_binary64`
13×	`neg-mul-1_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-rgt-in_binary64`
11×	`unsub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10

prune2.0ms (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

4.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	4.9b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 y (*.f64 z t))
4.9b	(/.f64 x (-.f64 y (*.f64 z t)))

rewrite51.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`times-frac_binary64`
4×	`add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l_binary64` `associate-/r_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`

Counts

2 → 41

Calls

2 calls:

5.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
3.0ms	(-.f64 y (*.f64 z t))

Compiler

Compiled 631 to 143 computations (77.3% saved)

series91.0ms (2%)

Error

4.9b

Counts

2 → 43

Calls

2 calls:

61.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
25.0ms	(-.f64 y (*.f64 z t))

Compiler

Compiled 1178 to 783 computations (33.5% saved)

simplify94.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

316×	`distribute-rgt-in_binary64`
300×	`div-sub_binary64`
258×	`cancel-sign-sub-inv_binary64`
257×	`associate-/l*_binary64`
237×	`times-frac_binary64`

Counts

84 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1277
1	236	1220
2	702	1178
3	2621	1130
4	4608	1130
5	5175	1130

prune43.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	6	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Error

4.8b

Counts

61 → 7

Alt Table

Status	Error	Program
	33.9b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 t z)) (sqrt.f64 x)))
	30.9b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 t z))) 3))
	31.9b	(.f64 (/.f64 x (-.f64 (.f64 y y) (.f64 (.f64 t z) (.f64 t z)))) (+.f64 y (.f64 z t)))
✓	4.9b	(/.f64 x (-.f64 y (*.f64 z t)))
▶	5.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
	5.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
	5.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 786 to 267 computations (66% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 y (*.f64 t z))
0.5b	(/.f64 1 (-.f64 y (*.f64 t z)))
4.7b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))

rewrite99.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

26×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `times-frac_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
15×	`associate-r_binary64`

Counts

3 → 83

Calls

3 calls:

9.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
4.0ms	(/.f64 1 (-.f64 y (*.f64 t z)))
3.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1405 to 540 computations (61.6% saved)

series146.0ms (3.3%)

Error

4.8b

Counts

3 → 65

Calls

3 calls:

63.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
47.0ms	(/.f64 1 (-.f64 y (*.f64 t z)))
25.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 2030 to 1407 computations (30.7% saved)

simplify105.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

563×	`times-frac_binary64`
388×	`cancel-sign-sub-inv_binary64`
386×	`associate-/l*_binary64`
323×	`associate-l_binary64`
292×	`unswap-sqr_binary64`

Counts

148 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2190
1	295	2042
2	944	1976
3	3617	1976
4	5207	1976

prune44.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	90	7	97

Error

4.8b

Counts

97 → 7

Alt Table

Status	Error	Program
	33.9b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 t z)) (sqrt.f64 x)))
	30.9b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 t z))) 3))
	31.9b	(.f64 (/.f64 x (-.f64 (.f64 y y) (.f64 (.f64 t z) (.f64 t z)))) (+.f64 y (.f64 z t)))
✓	4.9b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	5.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
▶	5.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
	5.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 845 to 312 computations (63.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 y (*.f64 t z))
0.7b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
4.8b	(/.f64 (-.f64 y (*.f64 t z)) x)

rewrite137.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

84×	`times-frac_binary64`
53×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
16×	`add-exp-log_binary64` `associate-/r*_binary64`
10×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`

Counts

3 → 118

Calls

3 calls:

7.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
5.0ms	(/.f64 (-.f64 y (*.f64 t z)) x)
3.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 2282 to 715 computations (68.7% saved)

series147.0ms (3.3%)

Error

4.8b

Counts

3 → 64

Calls

3 calls:

65.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
47.0ms	(/.f64 (-.f64 y (*.f64 t z)) x)
25.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1732 to 1175 computations (32.2% saved)

simplify160.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

594×	`times-frac_binary64`
398×	`associate-/l*_binary64`
385×	`associate-l_binary64`
294×	`associate-/r*_binary64`
269×	`associate-*l/_binary64`

Counts

182 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	3180
1	341	2922
2	1125	2855
3	4209	2855
4	4991	2855
5	4969	2855

prune44.0ms (1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	120	7	127

Error

4.8b

Counts

127 → 7

Alt Table

Status	Error	Program
	33.9b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 t z)) (sqrt.f64 x)))
	30.9b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 t z))) 3))
	31.9b	(.f64 (/.f64 x (-.f64 (.f64 y y) (.f64 (.f64 t z) (.f64 t z)))) (+.f64 y (.f64 z t)))
✓	4.9b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	5.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
✓	5.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
▶	5.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 1004 to 311 computations (69% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
10.1b	(cbrt.f64 (-.f64 y (*.f64 t z)))
10.1b	(cbrt.f64 (-.f64 y (*.f64 t z)))
10.1b	(cbrt.f64 (-.f64 y (*.f64 t z)))

rewrite97.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

18×	`cbrt-div_binary64`
15×	`add-exp-log_binary64`
12×	`pow1_binary64`
9×	`pow1/3_binary64` `add-cube-cbrt_binary64` `flip3--_binary64` `flip--_binary64` `cbrt-prod_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `pow-flip_binary64`
8×	`associate-/r/_binary64`

Counts

4 → 82

Calls

4 calls:

10.0ms	(/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))

Compiler

Compiled 2583 to 510 computations (80.3% saved)

series356.0ms (7.9%)

Error

4.8b

Counts

4 → 67

Calls

4 calls:

78.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
74.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
72.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
70.0ms	(/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 7134 to 4526 computations (36.6% saved)

simplify156.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

633×	`associate-/l*_binary64`
543×	`associate-/r*_binary64`
200×	`cancel-sign-sub-inv_binary64`
194×	`distribute-rgt-neg-in_binary64`
189×	`distribute-lft-neg-in_binary64`

Counts

149 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	3580
1	542	3323
2	1666	3192
3	4653	3114
4	4992	3114
5	4962	3114

prune83.0ms (1.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	108	8	116

Error

4.7b

Counts

116 → 8

Alt Table

Status	Error	Program
	27.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 x (/.f64 (cbrt.f64 (-.f64 (.f64 y y) (.f64 (.f64 t z) (.f64 t z)))) (cbrt.f64 (+.f64 (*.f64 t z) y)))))
	33.9b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 t z)) (sqrt.f64 x)))
	30.9b	(cbrt.f64 (pow.f64 (/.f64 x (-.f64 y (*.f64 t z))) 3))
	31.9b	(.f64 (/.f64 x (-.f64 (.f64 y y) (.f64 (.f64 t z) (.f64 t z)))) (+.f64 y (.f64 z t)))
	4.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	5.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
	5.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
	5.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 t z)))))

Compiler

Compiled 2701 to 971 computations (64.1% saved)

regimes707.0ms (15.8%)

Accuracy

Total 0.1b remaining (2.6%)

Threshold costs 0.1b (2.6%)

Compiler

Compiled 11917 to 6438 computations (46% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`sub-neg_binary64` `*-commutative_binary64` `+-commutative_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
1×	`distribute-lft-neg-out_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	30	10
4	34	10
5	35	10
6	35	10

end6.0ms (0.1%)

Remove: (sort z t)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample691.0ms (15.4%)

Algorithm

1×

intervals

Results

239.0ms	8000×	body	128	valid
9.0ms	338×	body	128	invalid

Compiler

Compiled 185 to 106 computations (42.7% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10

Details

analyze1.2s (25.7%)

sample24.0ms (0.5%)

simplify14.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite51.0ms (1.1%)

series91.0ms (2%)

simplify94.0ms (2.1%)

prune43.0ms (1%)

localize7.0ms (0.2%)

rewrite99.0ms (2.2%)

series146.0ms (3.3%)

simplify105.0ms (2.4%)

prune44.0ms (1%)

localize7.0ms (0.1%)

rewrite137.0ms (3.1%)

series147.0ms (3.3%)

simplify160.0ms (3.6%)

prune44.0ms (1%)

localize12.0ms (0.3%)

rewrite97.0ms (2.2%)

series356.0ms (7.9%)

simplify156.0ms (3.5%)

prune83.0ms (1.8%)

regimes707.0ms (15.8%)

simplify3.0ms (0.1%)

end6.0ms (0.1%)

sample691.0ms (15.4%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10