Details

analyze1.1s (10.7%)

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
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)

sample31.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	203×	body	128	valid
3.0ms	20×	body	1024	valid
2.0ms	51×	body	128	invalid
2.0ms	15×	body	512	valid
2.0ms	17×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4887	19
1	4887	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

Merged error: 23.6b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y z) (-.f64 t x))
2.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
13.9b	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`flip3--_binary64` `flip--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
8×	`associate-/l/_binary64` `frac-times_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 85

Calls

3 calls:

15.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
12.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
9.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

series942.0ms (9.4%)

Counts

3 → 9

Calls

3 calls:

501.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
367.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
74.0ms	(*.f64 (-.f64 y z) (-.f64 t x))

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	7026	1683

prune761.0ms (7.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	78	16	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	16	95

Merged error: 4.0b

Counts

95 → 16

Compiler

Compiled 15728 to 9658 computations (38.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
2.9b	(.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))))
9.6b	(+.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)))))

rewrite77.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
46×	`associate-r_binary64`
37×	`cbrt-prod_binary64`
27×	`add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`
18×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
17×	`associate-l_binary64`
16×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `unswap-sqr_binary64`
5×	`frac-times_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow1/3_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

47.0ms	(.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))))
5.0ms	(+.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))

series1.7s (17.3%)

Counts

4 → 12

Calls

4 calls:

754.0ms	(.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))))
523.0ms	(+.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)))))
238.0ms	(cbrt.f64 (-.f64 a z))
227.0ms	(cbrt.f64 (-.f64 a z))

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5584	3915

prune215.0ms (2.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	145	17	162

Merged error: 4.0b

Counts

162 → 17

Compiler

Compiled 5921 to 1625 computations (72.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
3.5b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
7.1b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

rewrite119.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

330×	`times-frac_binary64`
323×	`*-un-lft-identity_binary64`
321×	`add-sqr-sqrt_binary64`
113×	`add-cube-cbrt_binary64`
104×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
15×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `div-sub_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 274

Calls

3 calls:

52.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
18.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))
9.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

series1.4s (13.6%)

Counts

3 → 9

Calls

3 calls:

737.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))
505.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
125.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

simplify116.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5082	8418

prune356.0ms (3.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	279	4	283
Fresh	7	8	15
Picked	1	0	1
Done	0	1	1
Total	287	13	300

Merged error: 3.1b

Counts

300 → 13

Compiler

Compiled 9870 to 2654 computations (73.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
2.3b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)))
3.1b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x))

rewrite52.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64`
77×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`add-cube-cbrt_binary64` `associate-l_binary64`
23×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
12×	`cancel-sign-sub-inv_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `associate-r_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`sub-neg_binary64` `associate-/r/_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 135

Calls

3 calls:

23.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x))
9.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
5.0ms	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)))

series1.3s (12.8%)

Counts

3 → 9

Calls

3 calls:

712.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x))
496.0ms	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x)))
81.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5016	2791

prune154.0ms (1.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	143	14	157

Merged error: 3.0b

Counts

157 → 14

Compiler

Compiled 4005 to 1148 computations (71.3% saved)

regimes205.0ms (2%)

Compiler: Compiled 1485 to 950 computations (36% saved)

bsearch55.0ms (0.5%)

Steps

Iters	Range		Point
7	1.1667768483136998e-115	8.385883370377564e-114	1.5807917828594455e-115
8	-1.4669268829972057e-111	-4.511448938395734e-116	-5.284160521582155e-116

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	87
1	89	87

end0.0ms (0%)

sample1.1s (11%)

Algorithm

1×

intervals

Results

290.0ms	6657×	body	128	valid
75.0ms	398×	body	1024	valid
58.0ms	507×	body	512	valid
51.0ms	1158×	body	128	invalid
31.0ms	386×	body	256	valid
10.0ms	52×	body	2048	valid

Compiler

Compiled 406 to 246 computations (39.4% saved)

Details

analyze1.1s (10.7%)

sample31.0ms (0.3%)

simplify96.0ms (1%)

prune2.0ms (0%)

localize14.0ms (0.1%)

rewrite43.0ms (0.4%)

series942.0ms (9.4%)

simplify65.0ms (0.7%)

prune761.0ms (7.6%)

localize13.0ms (0.1%)

rewrite77.0ms (0.8%)

series1.7s (17.3%)

simplify66.0ms (0.7%)

prune215.0ms (2.1%)

localize9.0ms (0.1%)

rewrite119.0ms (1.2%)

series1.4s (13.6%)

simplify116.0ms (1.2%)

prune356.0ms (3.5%)

localize10.0ms (0.1%)

rewrite52.0ms (0.5%)

series1.3s (12.8%)

simplify73.0ms (0.7%)

prune154.0ms (1.5%)

regimes205.0ms (2%)

bsearch55.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.1s (11%)

Profiling