Details

analyze1.0s (10.8%)

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
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.2%	87.6%	0.2%	13
21.8%	77.8%	0.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

8.0ms	208×	body	128	valid
3.0ms	19×	body	1024	valid
2.0ms	15×	body	512	valid
1.0ms	31×	body	128	invalid
1.0ms	12×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify192.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4936	19
1	4936	19

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

24.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y z) (-.f64 t x))
2.9b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
17.0b	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_16809` `*-un-lft-identity_binary64_16787`
13×	`flip3--_binary64_16791` `flip--_binary64_16762`
10×	`add-exp-log_binary64_16825` `add-cbrt-cube_binary64_16823`
9×	`add-cube-cbrt_binary64_16822`
8×	`associate-/l/_binary64_16734` `frac-times_binary64_16797`
6×	`cancel-sign-sub-inv_binary64_16753`
5×	`associate-r_binary64_16727` `add-log-exp_binary64_16826` `times-frac_binary64_16793` `pow1_binary64_16848` `associate-l_binary64_16728` `associate-/r*_binary64_16731`
4×	`difference-of-squares_binary64_16756` `associate-r/_binary64_16729` `distribute-lft-out--_binary64_16739` `distribute-rgt-in_binary64_16737` `distribute-lft-in_binary64_16736` `associate-l/_binary64_16730`
2×	`cbrt-undiv_binary64_16821` `cbrt-unprod_binary64_16820` `sub-neg_binary64_16780` `prod-exp_binary64_16836` `div-exp_binary64_16838` `associate-/r/_binary64_16733`
1×	`associate-/l_binary64_16732` `sum-log_binary64_16878` `clear-num_binary64_16786` `-commutative_binary64_16718` `flip-+_binary64_16761` `distribute-lft-out_binary64_16738` `unswap-sqr_binary64_16755` `+-commutative_binary64_16717` `frac-2neg_binary64_16798` `div-inv_binary64_16784` `pow-prod-down_binary64_16858` `flip3-+_binary64_16790`

Counts

3 → 85

Calls

3 calls:

13.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
10.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

series439.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

233.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
170.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
37.0ms	(*.f64 (-.f64 y z) (-.f64 t x))

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5031	1683

prune103.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	13	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Error

4.8b

Counts

95 → 13

Compiler

Compiled 2099 to 555 computations (73.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a z))
0.5b	(cbrt.f64 (-.f64 a z))
2.2b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
10.0b	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite64.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64_16809`
59×	`*-un-lft-identity_binary64_16787`
52×	`times-frac_binary64_16793`
46×	`associate-r_binary64_16727`
37×	`cbrt-prod_binary64_16818`
27×	`add-cube-cbrt_binary64_16822`
25×	`add-exp-log_binary64_16825`
18×	`cbrt-div_binary64_16819` `add-cbrt-cube_binary64_16823`
17×	`associate-l_binary64_16728`
16×	`difference-of-squares_binary64_16756` `distribute-lft-out--_binary64_16739`
10×	`associate-/r/_binary64_16733`
9×	`flip3--_binary64_16791` `flip--_binary64_16762`
8×	`cbrt-unprod_binary64_16820` `prod-exp_binary64_16836`
7×	`cbrt-undiv_binary64_16821` `div-exp_binary64_16838`
6×	`add-log-exp_binary64_16826` `pow1_binary64_16848` `unswap-sqr_binary64_16755`
5×	`frac-times_binary64_16797`
3×	`associate-r/_binary64_16729` `associate-l/_binary64_16730`
2×	`pow1/3_binary64_16869` `div-inv_binary64_16784`
1×	`sum-log_binary64_16878` `*-commutative_binary64_16718` `flip-+_binary64_16761` `+-commutative_binary64_16717` `pow-prod-down_binary64_16858` `flip3-+_binary64_16790`

Counts

4 → 134

Calls

4 calls:

37.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
4.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))

series807.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

328.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
246.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
119.0ms	(cbrt.f64 (-.f64 a z))
114.0ms	(cbrt.f64 (-.f64 a z))

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5605	3915

prune152.0ms (1.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	145	14	159

Error

4.8b

Counts

159 → 14

Compiler

Compiled 4755 to 904 computations (81% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
2.0b	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
2.0b	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
10.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))))

rewrite60.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`cbrt-prod_binary64_16818`
39×	`cbrt-div_binary64_16819`
24×	`associate-/r/_binary64_16733`
18×	`flip3--_binary64_16791` `flip--_binary64_16762`
16×	`add-sqr-sqrt_binary64_16809` `*-un-lft-identity_binary64_16787`
15×	`times-frac_binary64_16793`
12×	`frac-times_binary64_16797`
10×	`add-cube-cbrt_binary64_16822`
6×	`add-log-exp_binary64_16826` `associate-r/_binary64_16729` `associate-l/_binary64_16730`
4×	`pow1_binary64_16848` `add-exp-log_binary64_16825` `add-cbrt-cube_binary64_16823`
3×	`difference-of-squares_binary64_16756` `distribute-lft-out--_binary64_16739` `pow1/3_binary64_16869` `div-inv_binary64_16784`
1×	`sum-log_binary64_16878` `flip-+_binary64_16761` `+-commutative_binary64_16717` `flip3-+_binary64_16790`

Counts

4 → 89

Calls

4 calls:

13.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
13.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
13.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
4.0ms	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))))

series1.6s (16.3%)

Counts

4 → 12

Calls

4 calls:

437.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
427.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
418.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
273.0ms	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))))

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4972	3603
1	4972	3603

prune158.0ms (1.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	100	15	115

Error

4.8b

Counts

115 → 15

Compiler

Compiled 6626 to 921 computations (86.1% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))) (.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))))
2.0b	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
2.0b	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
10.3b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))) (.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))))

rewrite114.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`cbrt-div_binary64_16819`
57×	`frac-times_binary64_16797`
40×	`add-exp-log_binary64_16825`
35×	`associate-*r/_binary64_16729`
34×	`cbrt-prod_binary64_16818`
31×	`associate-*l/_binary64_16730`
25×	`pow1_binary64_16848`
24×	`cbrt-unprod_binary64_16820` `prod-exp_binary64_16836`
19×	`add-cbrt-cube_binary64_16823`
16×	`associate-/r/_binary64_16733`
15×	`pow-prod-down_binary64_16858`
12×	`flip3--_binary64_16791` `add-sqr-sqrt_binary64_16809` `*-un-lft-identity_binary64_16787` `flip--_binary64_16762`
10×	`times-frac_binary64_16793`
8×	`add-cube-cbrt_binary64_16822`
6×	`add-log-exp_binary64_16826`
3×	`cbrt-undiv_binary64_16821` `div-exp_binary64_16838`
2×	`difference-of-squares_binary64_16756` `distribute-lft-out--_binary64_16739` `pow1/3_binary64_16869` `div-inv_binary64_16784`
1×	`associate-r_binary64_16727` `sum-log_binary64_16878` `-commutative_binary64_16718` `flip-+_binary64_16761` `associate-l*_binary64_16728` `+-commutative_binary64_16717` `flip3-+_binary64_16790`

Counts

4 → 128

Calls

4 calls:

55.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))) (.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))))
13.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
13.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
5.0ms	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))) (.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))))

series1.5s (15.4%)

Counts

4 → 12

Calls

4 calls:

429.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
419.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
355.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))) (.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))))
270.0ms	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))) (.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))))

simplify148.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4957	9622
1	4957	9622

prune203.0ms (2.1%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	138	17	155

Error

4.8b

Counts

155 → 17

Compiler

Compiled 10013 to 745 computations (92.6% saved)

regimes914.0ms (9.6%)

Accuracy

Total 6.0b remaining (64.2%)

Threshold costs 0b (0%)

Compiler

Compiled 9947 to 4961 computations (50.1% saved)

bsearch4.0ms (0%)

Compiler: Compiled 13 to 11 computations (15.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	152
1	83	152

end0.0ms (0%)

sample1.7s (18.1%)

Algorithm

1×

intervals

Results

270.0ms	6746×	body	128	valid
65.0ms	369×	body	1024	valid
60.0ms	1233×	body	128	invalid
51.0ms	472×	body	512	valid
33.0ms	343×	body	256	valid
13.0ms	70×	body	2048	valid

Compiler

Compiled 1793 to 876 computations (51.1% saved)

Details

analyze1.0s (10.8%)

sample27.0ms (0.3%)

simplify192.0ms (2%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite38.0ms (0.4%)

series439.0ms (4.6%)

simplify66.0ms (0.7%)

prune103.0ms (1.1%)

localize16.0ms (0.2%)

rewrite64.0ms (0.7%)

series807.0ms (8.5%)

simplify74.0ms (0.8%)

prune152.0ms (1.6%)

localize22.0ms (0.2%)

rewrite60.0ms (0.6%)

series1.6s (16.3%)

simplify104.0ms (1.1%)

prune158.0ms (1.7%)

localize34.0ms (0.4%)

rewrite114.0ms (1.2%)

series1.5s (15.4%)

simplify148.0ms (1.5%)

prune203.0ms (2.1%)

regimes914.0ms (9.6%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.7s (18.1%)

Profiling