Details

analyze372.0ms (7.1%)

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%	68.6%	31.4%	5
0%	65.5%	34.5%	6
0%	59.2%	40.8%	7
0%	51.4%	48.6%	8
0%	41.3%	58.7%	9
0%	28.4%	71.6%	10
2.3%	22.3%	75.4%	11
2.3%	21%	76.7%	12
2.7%	18%	79.3%	13
2.7%	16.4%	80.8%	14

Compiler

Compiled 17 to 16 computations (5.9% saved)

sample42.0ms (0.8%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	123×	body	80	nan
0.0ms	1×	body	80	invalid

Compiler

Compiled 33 to 36 computations (-9.1% saved)

simplify213.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (200.0ms)

Iter	Nodes	Cost
0	4940	25
1	4940	25

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: 0.3b

Counts

2 → 1

Compiler

Compiled 32 to 30 computations (6.3% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
0.1b	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
0.2b	(*.f64 (-.f64 a 1/2) (log.f64 t))
0.6b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
19×	`log-prod_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64`
14×	`add-log-exp_binary64`
12×	`add-cube-cbrt_binary64`
9×	`distribute-lft-out_binary64` `log-pow_binary64` `associate-+r+_binary64`
6×	`flip3--_binary64` `associate-+l+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate-*l/_binary64` `sum-log_binary64`
5×	`associate-l_binary64` `associate-+l-_binary64`
4×	`flip3-+_binary64` `diff-log_binary64` `associate-r_binary64` `frac-add_binary64` `log-div_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `associate--l-_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

14.0ms	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
9.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
8.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
8.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))

series108.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
30.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
15.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
10.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))

simplify90.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4983	2413
1	4983	2413

prune128.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 0.0b

Counts

113 → 8

Compiler

Compiled 2880 to 1136 computations (60.6% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
0.5b	(cbrt.f64 (+.f64 x y))
0.5b	(cbrt.f64 (+.f64 x y))
0.5b	(cbrt.f64 (+.f64 x y))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64`
35×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `swap-sqr_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `flip-+_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

11.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
4.0ms	(cbrt.f64 (+.f64 x y))
3.0ms	(cbrt.f64 (+.f64 x y))
3.0ms	(cbrt.f64 (+.f64 x y))

series141.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
34.0ms	(cbrt.f64 (+.f64 x y))
31.0ms	(cbrt.f64 (+.f64 x y))
30.0ms	(cbrt.f64 (+.f64 x y))

simplify72.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5177	1542

prune104.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	107	8	115

Merged error: 0.0b

Counts

115 → 8

Compiler

Compiled 3759 to 1336 computations (64.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) t)
0.1b	(+.f64 (log.f64 z) (-.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) t))
0.1b	(+.f64 (log.f64 (+.f64 x y)) (+.f64 (log.f64 z) (-.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) t)))
0.2b	(*.f64 (-.f64 a 1/2) (log.f64 t))

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
25×	`log-prod_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
13×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out_binary64`
12×	`associate--l+_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
8×	`associate-+r+_binary64`
7×	`log-pow_binary64` `associate-+l+_binary64` `sum-log_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-l_binary64`
4×	`associate-r_binary64`
3×	`flip3-+_binary64` `associate-+r-_binary64` `diff-log_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `associate-+l-_binary64` `log-div_binary64` `+-commutative_binary64` `flip--_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

15.0ms	(+.f64 (log.f64 (+.f64 x y)) (+.f64 (log.f64 z) (-.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) t)))
10.0ms	(+.f64 (log.f64 z) (-.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) t))
9.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))
8.0ms	(-.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) t)

series94.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(+.f64 (log.f64 (+.f64 x y)) (+.f64 (log.f64 z) (-.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) t)))
21.0ms	(+.f64 (log.f64 z) (-.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) t))
12.0ms	(*.f64 (-.f64 a 1/2) (log.f64 t))
10.0ms	(-.f64 (*.f64 (-.f64 a 1/2) (log.f64 t)) t)

simplify60.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4999	2247
1	4999	2247

prune93.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	110	8	118

Merged error: 0.0b

Counts

118 → 8

Compiler

Compiled 2667 to 1286 computations (51.8% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (cbrt.f64 t))))
0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
0.6b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`log-prod_binary64`
30×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
28×	`associate-+l+_binary64`
26×	`*-un-lft-identity_binary64`
24×	`cbrt-prod_binary64`
20×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`associate-+r+_binary64`
8×	`pow1_binary64` `associate-*l/_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out_binary64`
4×	`flip3--_binary64` `frac-add_binary64` `log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`pow1/3_binary64` `associate-+l-_binary64` `log-div_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

16.0ms	(+.f64 (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (cbrt.f64 t))))
8.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)

series85.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(+.f64 (.f64 (-.f64 a 1/2) (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 (-.f64 a 1/2) (log.f64 (cbrt.f64 t))))
18.0ms	(cbrt.f64 t)
15.0ms	(cbrt.f64 t)
14.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5245	1779

prune95.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	108	10	118

Merged error: 0b

Counts

118 → 10

Compiler

Compiled 3500 to 1510 computations (56.9% saved)

regimes832.0ms (16%)

Compiler: Compiled 3280 to 2699 computations (17.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	45
1	43	45

end0.0ms (0%)

sample2.4s (46%)

Algorithm

1×

intervals

Results

603.0ms	8000×	body	80	valid
297.0ms	4304×	body	80	nan
2.0ms	33×	body	80	invalid

Compiler

Compiled 337 to 274 computations (18.7% saved)

Details

analyze372.0ms (7.1%)

sample42.0ms (0.8%)

simplify213.0ms (4.1%)

prune7.0ms (0.1%)

localize15.0ms (0.3%)

rewrite42.0ms (0.8%)

series108.0ms (2.1%)

simplify90.0ms (1.7%)

prune128.0ms (2.5%)

localize22.0ms (0.4%)

rewrite25.0ms (0.5%)

series141.0ms (2.7%)

simplify72.0ms (1.4%)

prune104.0ms (2%)

localize15.0ms (0.3%)

rewrite46.0ms (0.9%)

series94.0ms (1.8%)

simplify60.0ms (1.2%)

prune93.0ms (1.8%)

localize19.0ms (0.4%)

rewrite30.0ms (0.6%)

series85.0ms (1.6%)

simplify57.0ms (1.1%)

prune95.0ms (1.8%)

regimes832.0ms (16%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.4s (46%)

Profiling