Details

analyze707.0ms (12.7%)

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
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample21.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 35 to 33 computations (5.7% saved)

simplify233.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4903	19
1	4903	19

prune4.0ms (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: 2.0b

Counts

2 → 2

Compiler

Compiled 43 to 36 computations (16.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
0.0b	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
4.1b	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
6.5b	(/.f64 (.f64 y t) (.f64 2 z))

rewrite55.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_14400`
25×	`add-sqr-sqrt_binary64_14422`
18×	`add-exp-log_binary64_14438` `add-cbrt-cube_binary64_14436`
16×	`times-frac_binary64_14406`
15×	`add-cube-cbrt_binary64_14435`
8×	`add-log-exp_binary64_14439`
6×	`associate-/r*_binary64_14344`
5×	`cbrt-undiv_binary64_14434` `difference-of-squares_binary64_14369` `div-exp_binary64_14451` `distribute-lft-out--_binary64_14352`
4×	`cbrt-unprod_binary64_14433` `prod-exp_binary64_14449` `pow1_binary64_14461` `associate-/l*_binary64_14345`
3×	`cancel-sign-sub-inv_binary64_14366`
2×	`frac-2neg_binary64_14411` `clear-num_binary64_14399` `flip--_binary64_14375` `div-inv_binary64_14397` `flip3--_binary64_14404` `associate-/r/_binary64_14346`
1×	`sub-neg_binary64_14393` `+-commutative_binary64_14330` `flip3-+_binary64_14403` `distribute-lft-out_binary64_14351` `flip-+_binary64_14374` `diff-log_binary64_14492` `sum-log_binary64_14491`

Counts

4 → 86

Calls

4 calls:

20.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
11.0ms	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
9.0ms	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
7.0ms	(/.f64 (.f64 y t) (.f64 2 z))

series380.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
111.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
89.0ms	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
45.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4945	1905
1	4945	1905

prune107.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	94	6	100

Merged error: 0.2b

Counts

100 → 6

Compiler

Compiled 1999 to 1029 computations (48.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)
0.6b	(/.f64 2 (/.f64 t z))
4.1b	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
6.5b	(/.f64 y (/.f64 2 (/.f64 t z)))

rewrite187.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

525×	`times-frac_binary64_14406`
315×	`add-sqr-sqrt_binary64_14422`
255×	`*-un-lft-identity_binary64_14400`
245×	`add-cube-cbrt_binary64_14435`
65×	`associate-/r*_binary64_14344`
23×	`div-inv_binary64_14397`
20×	`add-exp-log_binary64_14438` `difference-of-squares_binary64_14369` `add-cbrt-cube_binary64_14436`
10×	`cbrt-undiv_binary64_14434` `div-exp_binary64_14451`
9×	`associate-/l*_binary64_14345`
8×	`associate-/r/_binary64_14346`
6×	`add-log-exp_binary64_14439`
5×	`distribute-lft-out--_binary64_14352`
4×	`pow1_binary64_14461`
3×	`cancel-sign-sub-inv_binary64_14366` `frac-2neg_binary64_14411` `clear-num_binary64_14399`
2×	`flip--_binary64_14375` `flip3--_binary64_14404`
1×	`sub-neg_binary64_14393` `diff-log_binary64_14492`

Counts

4 → 334

Calls

4 calls:

60.0ms	(-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)
55.0ms	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
15.0ms	(/.f64 y (/.f64 2 (/.f64 t z)))
7.0ms	(/.f64 2 (/.f64 t z))

series301.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
85.0ms	(-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)
44.0ms	(/.f64 y (/.f64 2 (/.f64 t z)))
27.0ms	(/.f64 2 (/.f64 t z))

simplify141.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4942	8126
1	4942	8126

prune353.0ms (6.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	346	0	346
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	346	6	352

Merged error: 0.2b

Counts

352 → 6

Compiler

Compiled 8172 to 3738 computations (54.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
0.4b	(/.f64 1 (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
3.9b	(.f64 y (/.f64 1 (-.f64 (/.f64 (.f64 y t) (*.f64 2 z)) z)))
6.5b	(/.f64 (.f64 y t) (.f64 2 z))

rewrite61.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_14422`
42×	`*-un-lft-identity_binary64_14400`
33×	`times-frac_binary64_14406`
29×	`add-exp-log_binary64_14438`
25×	`add-cube-cbrt_binary64_14435`
23×	`add-cbrt-cube_binary64_14436`
21×	`associate-r_binary64_14340`
8×	`prod-exp_binary64_14449` `difference-of-squares_binary64_14369` `div-exp_binary64_14451` `distribute-lft-out--_binary64_14352`
7×	`pow1_binary64_14461`
6×	`associate-/r*_binary64_14344` `cbrt-unprod_binary64_14433` `cbrt-undiv_binary64_14434` `add-log-exp_binary64_14439`
4×	`associate-/r/_binary64_14346` `associate-/l*_binary64_14345`
3×	`cancel-sign-sub-inv_binary64_14366` `flip--_binary64_14375` `div-inv_binary64_14397` `flip3--_binary64_14404` `associate-l_binary64_14341` `unswap-sqr_binary64_14368`
2×	`1-exp_binary64_14444` `frac-2neg_binary64_14411` `clear-num_binary64_14399` `rec-exp_binary64_14450`
1×	`sub-neg_binary64_14393` `pow-prod-down_binary64_14471` `pow-flip_binary64_14474` `associate-r/_binary64_14342` `diff-log_binary64_14492` `-commutative_binary64_14331` `un-div-inv_binary64_14398` `inv-pow_binary64_14485`

Counts

4 → 122

Calls

4 calls:

19.0ms	(.f64 y (/.f64 1 (-.f64 (/.f64 (.f64 y t) (*.f64 2 z)) z)))
12.0ms	(/.f64 1 (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
9.0ms	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
6.0ms	(/.f64 (.f64 y t) (.f64 2 z))

series368.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(.f64 y (/.f64 1 (-.f64 (/.f64 (.f64 y t) (*.f64 2 z)) z)))
109.0ms	(/.f64 1 (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
87.0ms	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
46.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4946	2410
1	4946	2410

prune134.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	134	6	140

Merged error: 0.2b

Counts

140 → 6

Compiler

Compiled 2935 to 1660 computations (43.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.6b	(/.f64 (cbrt.f64 y) (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
2.8b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
6.5b	(/.f64 (.f64 y t) (.f64 2 z))

rewrite76.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-sqr-sqrt_binary64_14422`
74×	`*-un-lft-identity_binary64_14400`
63×	`times-frac_binary64_14406`
50×	`cbrt-prod_binary64_14431`
48×	`add-cube-cbrt_binary64_14435`
42×	`associate-r_binary64_14340`
32×	`add-exp-log_binary64_14438`
23×	`add-cbrt-cube_binary64_14436`
16×	`pow1_binary64_14461`
13×	`difference-of-squares_binary64_14369` `distribute-lft-out--_binary64_14352`
11×	`cbrt-unprod_binary64_14433` `prod-exp_binary64_14449`
7×	`cbrt-undiv_binary64_14434` `div-exp_binary64_14451` `associate-l_binary64_14341` `unswap-sqr_binary64_14368` `associate-/l*_binary64_14345`
6×	`associate-/r*_binary64_14344` `pow1/3_binary64_14482` `swap-sqr_binary64_14367`
5×	`pow-prod-down_binary64_14471`
4×	`add-log-exp_binary64_14439` `associate-/r/_binary64_14346`
3×	`div-inv_binary64_14397`
2×	`frac-2neg_binary64_14411` `clear-num_binary64_14399` `flip--_binary64_14375` `flip3--_binary64_14404` `pow-prod-up_binary64_14470` `pow-sqr_binary64_14373` `*-commutative_binary64_14331`
1×	`pow-plus_binary64_14463` `pow2_binary64_14481` `associate-*r/_binary64_14342`

Counts

4 → 175

Calls

4 calls:

26.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
12.0ms	(/.f64 (cbrt.f64 y) (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
10.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
6.0ms	(/.f64 (.f64 y t) (.f64 2 z))

series777.0ms (14%)

Counts

4 → 12

Calls

4 calls:

358.0ms	(/.f64 (cbrt.f64 y) (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
190.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
185.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
43.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify101.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4970	3658
1	4970	3658

prune207.0ms (3.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	187	6	193

Merged error: 0.2b

Counts

193 → 6

Compiler

Compiled 4889 to 2176 computations (55.5% saved)

regimes211.0ms (3.8%)

Compiler: Compiled 1845 to 1552 computations (15.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample924.0ms (16.6%)

Algorithm

1×

intervals

Results

382.0ms

8000×

body

128

valid

Compiler

Compiled 331 to 278 computations (16% saved)

Details

analyze707.0ms (12.7%)

sample21.0ms (0.4%)

simplify233.0ms (4.2%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite55.0ms (1%)

series380.0ms (6.8%)

simplify90.0ms (1.6%)

prune107.0ms (1.9%)

localize10.0ms (0.2%)

rewrite187.0ms (3.4%)

series301.0ms (5.4%)

simplify141.0ms (2.5%)

prune353.0ms (6.4%)

localize11.0ms (0.2%)

rewrite61.0ms (1.1%)

series368.0ms (6.6%)

simplify71.0ms (1.3%)

prune134.0ms (2.4%)

localize13.0ms (0.2%)

rewrite76.0ms (1.4%)

series777.0ms (14%)

simplify101.0ms (1.8%)

prune207.0ms (3.7%)

regimes211.0ms (3.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample924.0ms (16.6%)

Profiling