Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample31.0ms (1.2%)

Algorithm

1×

intervals

Results

13.0ms	65×	body	2048	valid
6.0ms	138×	body	128	valid
4.0ms	26×	body	1024	valid
2.0ms	22×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify172.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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: 15.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

2.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-sqr-sqrt_binary64_1109` `add-log-exp_binary64_1124` `*-un-lft-identity_binary64_1088`
1×	`diff-atan_binary64_1242` `add-cbrt-cube_binary64_1121` `flip3--_binary64_1092` `sub-neg_binary64_1081` `flip--_binary64_1063` `add-exp-log_binary64_1123` `diff-log_binary64_1177` `pow1_binary64_1146` `distribute-lft-out--_binary64_1042` `add-cube-cbrt_binary64_1120` `difference-of-squares_binary64_1057`

Counts

1 → 14

Calls

1 calls:

4.0ms

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series24.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

24.0ms

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify86.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5599	291

prune17.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	16	2	18

Merged error: 0.3b

Counts

18 → 2

Compiler

Compiled 256 to 170 computations (33.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0b	(*.f64 N (+.f64 N 1))
0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_1109` `*-un-lft-identity_binary64_1088`
5×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `add-log-exp_binary64_1124` `pow1_binary64_1146` `add-cube-cbrt_binary64_1120`
4×	`associate-r_binary64_1030`
3×	`associate-l_binary64_1031`
2×	`distribute-rgt-in_binary64_1040` `associate-+r+_binary64_1022` `flip-+_binary64_1062` `flip3-+_binary64_1091` `distribute-lft-in_binary64_1039` `associate-*r/_binary64_1032`
1×	`*-commutative_binary64_1021` `unswap-sqr_binary64_1056` `cbrt-unprod_binary64_1118` `sum-log_binary64_1176` `+-commutative_binary64_1020` `pow-prod-down_binary64_1156` `prod-exp_binary64_1134` `distribute-lft-out_binary64_1041`

Counts

3 → 43

Calls

3 calls:

9.0ms	(*.f64 N (+.f64 N 1))
4.0ms	(+.f64 1 (*.f64 N (+.f64 N 1)))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series85.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

55.0ms	(*.f64 N (+.f64 N 1))
16.0ms	(+.f64 1 (*.f64 N (+.f64 N 1)))
14.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify88.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4899	599
1	4899	599

prune56.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	45	7	52
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	47	7	54

Merged error: 0.3b

Counts

54 → 7

Compiler

Compiled 806 to 633 computations (21.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (+.f64 (*.f64 N N) N))
0.0b	(+.f64 (*.f64 N N) N)
0.3b	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_1124`
6×	`*-un-lft-identity_binary64_1088`
4×	`sum-log_binary64_1176`
3×	`add-cbrt-cube_binary64_1121` `add-sqr-sqrt_binary64_1109` `add-exp-log_binary64_1123` `pow1_binary64_1146` `add-cube-cbrt_binary64_1120`
2×	`+-commutative_binary64_1020` `flip-+_binary64_1062` `flip3-+_binary64_1091`
1×	`associate-+r+_binary64_1022` `distribute-lft1-in_binary64_1045` `distribute-rgt-out_binary64_1043` `distribute-lft-out_binary64_1041`

Counts

3 → 34

Calls

3 calls:

7.0ms	(+.f64 1 (+.f64 (*.f64 N N) N))
4.0ms	(+.f64 (*.f64 N N) N)
1.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

series86.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

54.0ms	(+.f64 (*.f64 N N) N)
18.0ms	(+.f64 1 (+.f64 (*.f64 N N) N))
13.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

simplify79.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4888	549
1	4888	549

prune35.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	43	7	50

Merged error: 0.3b

Counts

50 → 7

Compiler

Compiled 677 to 388 computations (42.7% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
14.2b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
14.2b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1109`
24×	`sqrt-prod_binary64_1103`
21×	`pow1_binary64_1146`
14×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
10×	`sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
8×	`swap-sqr_binary64_1055`
6×	`associate-r_binary64_1030` `add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `associate-l_binary64_1031`
5×	`pow-prod-up_binary64_1155`
4×	`unswap-sqr_binary64_1056` `add-log-exp_binary64_1124`
3×	`pow-prod-down_binary64_1156` `pow-sqr_binary64_1061`
2×	`rem-sqrt-square_binary64_1101`
1×	`*-commutative_binary64_1021` `pow-plus_binary64_1148` `cbrt-unprod_binary64_1118` `pow2_binary64_1166` `rem-square-sqrt_binary64_1100` `sqrt-unprod_binary64_1107` `prod-exp_binary64_1134`

Counts

4 → 82

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
2.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

series118.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
44.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
17.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
12.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify64.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5063	1485

prune326.0ms (12.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	92	9	101

Merged error: 0.2b

Counts

101 → 9

Compiler

Compiled 1971 to 1622 computations (17.7% saved)

regimes22.0ms (0.9%)

Compiler: Compiled 211 to 181 computations (14.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

end0.0ms (0%)

sample1.2s (46.7%)

Algorithm

1×

intervals

Results

424.0ms	2080×	body	2048	valid
175.0ms	4113×	body	128	valid
152.0ms	1034×	body	1024	valid
56.0ms	513×	body	512	valid
20.0ms	260×	body	256	valid

Compiler

Compiled 236 to 203 computations (14% saved)

Details

analyze1.0ms (0.1%)

sample31.0ms (1.2%)

simplify172.0ms (6.7%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite5.0ms (0.2%)

series24.0ms (0.9%)

simplify86.0ms (3.3%)

prune17.0ms (0.6%)

localize6.0ms (0.2%)

rewrite16.0ms (0.6%)

series85.0ms (3.3%)

simplify88.0ms (3.4%)

prune56.0ms (2.2%)

localize6.0ms (0.2%)

rewrite14.0ms (0.6%)

series86.0ms (3.3%)

simplify79.0ms (3.1%)

prune35.0ms (1.4%)

localize10.0ms (0.4%)

rewrite18.0ms (0.7%)

series118.0ms (4.6%)

simplify64.0ms (2.5%)

prune326.0ms (12.7%)

regimes22.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (46.7%)

Profiling