Details

analyze1.0s (10.5%)

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	213×	body	128	valid
2.0ms	15×	body	1024	valid
2.0ms	16×	body	512	valid
1.0ms	35×	body	128	invalid
1.0ms	9×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify246.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4851	19
1	4851	19

prune7.0ms (0.1%)

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: 27.2b

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))
2.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
19.7b	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_19286` `add-sqr-sqrt_binary64_19307`
13×	`flip--_binary64_19261` `flip3--_binary64_19290`
10×	`add-cbrt-cube_binary64_19319` `add-exp-log_binary64_19321`
8×	`associate-/l/_binary64_19235` `frac-times_binary64_19296`
7×	`add-cube-cbrt_binary64_19318`
5×	`times-frac_binary64_19292` `add-log-exp_binary64_19322` `associate-l_binary64_19229` `associate-/r_binary64_19232` `associate-r*_binary64_19228` `pow1_binary64_19344`
4×	`associate-r/_binary64_19230` `difference-of-squares_binary64_19255` `associate-l/_binary64_19231` `distribute-lft-out--_binary64_19240`
2×	`cbrt-undiv_binary64_19317` `prod-exp_binary64_19332` `associate-/r/_binary64_19234` `cbrt-unprod_binary64_19316` `sub-neg_binary64_19279` `div-exp_binary64_19334`
1×	`distribute-lft-out_binary64_19239` `clear-num_binary64_19285` `div-inv_binary64_19283` `associate-/l_binary64_19233` `pow-prod-down_binary64_19354` `distribute-rgt-in_binary64_19238` `sum-log_binary64_19374` `-commutative_binary64_19219` `distribute-lft-in_binary64_19237` `flip-+_binary64_19260` `+-commutative_binary64_19218` `flip3-+_binary64_19289` `frac-2neg_binary64_19297` `unswap-sqr_binary64_19254`

Counts

3 → 79

Calls

3 calls:

15.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
11.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
10.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

series932.0ms (9.6%)

Counts

3 → 9

Calls

3 calls:

502.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
359.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
70.0ms	(*.f64 (-.f64 y z) (-.f64 t x))

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	6742	1599

prune104.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	12	89

Merged error: 4.2b

Counts

89 → 12

Compiler

Compiled 1981 to 556 computations (71.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a z))
0.6b	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
1.5b	(.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))))
8.8b	(+.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)))))

rewrite96.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64_19307`
78×	`*-un-lft-identity_binary64_19286`
60×	`cbrt-prod_binary64_19314`
54×	`associate-r_binary64_19228`
52×	`times-frac_binary64_19292`
34×	`add-cube-cbrt_binary64_19318`
28×	`cbrt-div_binary64_19315`
27×	`add-exp-log_binary64_19321`
25×	`associate-l_binary64_19229`
21×	`distribute-lft-out--_binary64_19240`
19×	`difference-of-squares_binary64_19255`
18×	`add-cbrt-cube_binary64_19319`
14×	`flip--_binary64_19261` `flip3--_binary64_19290`
13×	`pow1_binary64_19344`
10×	`swap-sqr_binary64_19253` `associate-/r/_binary64_19234` `unswap-sqr_binary64_19254`
9×	`prod-exp_binary64_19332` `frac-times_binary64_19296` `cbrt-unprod_binary64_19316`
7×	`cbrt-undiv_binary64_19317` `pow1/3_binary64_19365` `div-exp_binary64_19334`
6×	`add-log-exp_binary64_19322`
5×	`associate-r/_binary64_19230` `associate-l/_binary64_19231`
3×	`pow-prod-down_binary64_19354`
2×	`pow-prod-up_binary64_19353` `div-inv_binary64_19283` `pow-sqr_binary64_19259` `*-commutative_binary64_19219`
1×	`sum-log_binary64_19374` `pow-plus_binary64_19346` `flip-+_binary64_19260` `pow2_binary64_19364` `+-commutative_binary64_19218` `flip3-+_binary64_19289`

Counts

4 → 175

Calls

4 calls:

50.0ms	(.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))))
13.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (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)))))
4.0ms	(cbrt.f64 (-.f64 a z))

series1.7s (17.8%)

Counts

4 → 12

Calls

4 calls:

746.0ms	(.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))))
525.0ms	(+.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)))))
232.0ms	(cbrt.f64 (-.f64 a z))
232.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5463	4490

prune194.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	187	12	199

Merged error: 4.2b

Counts

199 → 12

Compiler

Compiled 5745 to 1372 computations (76.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
2.9b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
6.4b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite52.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64_19307`
73×	`*-un-lft-identity_binary64_19286`
51×	`times-frac_binary64_19292`
31×	`associate-r_binary64_19228`
27×	`add-cube-cbrt_binary64_19318`
23×	`difference-of-squares_binary64_19255` `distribute-lft-out--_binary64_19240`
10×	`add-cbrt-cube_binary64_19319` `add-exp-log_binary64_19321`
5×	`associate-/l_binary64_19233` `add-log-exp_binary64_19322` `associate-l_binary64_19229` `associate-/r_binary64_19232` `flip--_binary64_19261` `pow1_binary64_19344` `flip3--_binary64_19290`
4×	`associate-/r/_binary64_19234`
2×	`div-inv_binary64_19283` `associate-/l/_binary64_19235` `cbrt-undiv_binary64_19317` `prod-exp_binary64_19332` `frac-times_binary64_19296` `cbrt-unprod_binary64_19316` `div-exp_binary64_19334` `unswap-sqr_binary64_19254` `associate-*l/_binary64_19231`
1×	`clear-num_binary64_19285` `pow-prod-down_binary64_19354` `div-sub_binary64_19291` `associate-r/_binary64_19230` `sum-log_binary64_19374` `-commutative_binary64_19219` `flip-+_binary64_19260` `+-commutative_binary64_19218` `flip3-+_binary64_19289` `frac-2neg_binary64_19297`

Counts

3 → 119

Calls

3 calls:

26.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
9.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
4.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

series999.0ms (10.3%)

Counts

3 → 9

Calls

3 calls:

513.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
350.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
136.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5636	2420

prune117.0ms (1.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	126	14	140

Merged error: 4.2b

Counts

140 → 14

Compiler

Compiled 2937 to 646 computations (78% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 t x))
0.6b	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
1.2b	(.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
7.3b	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

rewrite77.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_19307`
33×	`*-un-lft-identity_binary64_19286` `cbrt-prod_binary64_19314`
26×	`cbrt-div_binary64_19315`
24×	`add-exp-log_binary64_19321`
21×	`associate-r_binary64_19228`
15×	`flip--_binary64_19261` `add-cube-cbrt_binary64_19318` `flip3--_binary64_19290`
14×	`add-cbrt-cube_binary64_19319`
13×	`associate-l_binary64_19229` `pow1_binary64_19344`
10×	`swap-sqr_binary64_19253` `prod-exp_binary64_19332` `frac-times_binary64_19296` `cbrt-unprod_binary64_19316`
8×	`associate-/r/_binary64_19234` `distribute-lft-out--_binary64_19240`
7×	`pow1/3_binary64_19365`
6×	`add-log-exp_binary64_19322` `difference-of-squares_binary64_19255` `unswap-sqr_binary64_19254` `associate-*l/_binary64_19231`
5×	`associate-*r/_binary64_19230`
4×	`cbrt-undiv_binary64_19317` `div-exp_binary64_19334`
3×	`pow-prod-down_binary64_19354`
2×	`pow-prod-up_binary64_19353` `times-frac_binary64_19292` `pow-sqr_binary64_19259` `*-commutative_binary64_19219`
1×	`div-inv_binary64_19283` `sum-log_binary64_19374` `pow-plus_binary64_19346` `flip-+_binary64_19260` `pow2_binary64_19364` `+-commutative_binary64_19218` `flip3-+_binary64_19289`

Counts

4 → 126

Calls

4 calls:

34.0ms	(.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
14.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
6.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))
4.0ms	(cbrt.f64 (-.f64 t x))

series2.2s (22.2%)

Counts

4 → 12

Calls

4 calls:

1.2s	(.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
546.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))
234.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
217.0ms	(cbrt.f64 (-.f64 t x))

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4962	3239
1	4962	3239

prune152.0ms (1.6%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	138	14	152

Merged error: 4.2b

Counts

152 → 14

Compiler

Compiled 5439 to 1063 computations (80.5% saved)

regimes200.0ms (2.1%)

Compiler: Compiled 1755 to 1050 computations (40.2% saved)

bsearch108.0ms (1.1%)

Steps

Iters	Range		Point
8	4.598283063812728e+208	2.7054834286241125e+213	3.558503535078779e+212
8	4.956740803457661e+148	9.135345027284547e+151	1.0088239616805826e+149
10	9.734347643025362e+53	8.515699878330277e+72	6.37987987931022e+72
7	-3.1430961518231874e+195	-2.550071003841477e+193	-1.0460208328950513e+194

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	95	99
1	95	99

end0.0ms (0%)

sample1.1s (11.3%)

Algorithm

1×

intervals

Results

279.0ms	6720×	body	128	valid
56.0ms	396×	body	1024	valid
55.0ms	487×	body	512	valid
52.0ms	1264×	body	128	invalid
31.0ms	332×	body	256	valid
12.0ms	65×	body	2048	valid

Compiler

Compiled 466 to 273 computations (41.4% saved)

Details

analyze1.0s (10.5%)

sample27.0ms (0.3%)

simplify246.0ms (2.5%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite44.0ms (0.4%)

series932.0ms (9.6%)

simplify66.0ms (0.7%)

prune104.0ms (1.1%)

localize13.0ms (0.1%)

rewrite96.0ms (1%)

series1.7s (17.8%)

simplify82.0ms (0.8%)

prune194.0ms (2%)

localize9.0ms (0.1%)

rewrite52.0ms (0.5%)

series999.0ms (10.3%)

simplify72.0ms (0.7%)

prune117.0ms (1.2%)

localize18.0ms (0.2%)

rewrite77.0ms (0.8%)

series2.2s (22.2%)

simplify83.0ms (0.9%)

prune152.0ms (1.6%)

regimes200.0ms (2.1%)

bsearch108.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.1s (11.3%)

Profiling