Details

analyze1.6s (12.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.2%	98.5%	0.3%	13
1.8%	97.9%	0.3%	14

Compiler

Compiled 18 to 18 computations (0% saved)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
7.0ms	125×	body	128	invalid

Compiler

Compiled 35 to 42 computations (-20% saved)

simplify231.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	868	25
1	868	25

prune3.0ms (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: 0.0b

Counts

2 → 1

Compiler

Compiled 34 to 34 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
0.0b	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-log-exp_binary64_1150`
14×	`cancel-sign-sub-inv_binary64_1077`
13×	`*-un-lft-identity_binary64_1111`
9×	`associate-+l+_binary64_1044`
8×	`add-sqr-sqrt_binary64_1133`
6×	`times-frac_binary64_1117` `add-cube-cbrt_binary64_1146`
5×	`sum-log_binary64_1202`
4×	`diff-log_binary64_1203`
2×	`frac-sub_binary64_1120` `add-cbrt-cube_binary64_1147` `div-inv_binary64_1108` `flip-+_binary64_1085` `flip3-+_binary64_1114` `associate--l+_binary64_1048` `distribute-lft-out_binary64_1062` `pow1_binary64_1172` `sub-neg_binary64_1104` `distribute-lft-out--_binary64_1063` `add-exp-log_binary64_1149`
1×	`associate-+l-_binary64_1046` `flip3--_binary64_1115` `+-commutative_binary64_1041` `difference-of-squares_binary64_1080` `flip--_binary64_1086`

Counts

2 → 49

Calls

2 calls:

16.0ms	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
13.0ms	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

series483.0ms (3.8%)

Counts

2 → 6

Calls

2 calls:

307.0ms	(+.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
175.0ms	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5038	1426

prune87.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	4	56

Merged error: 0.0b

Counts

56 → 4

Compiler

Compiled 1936 to 1113 computations (42.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))
0.0b	(sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))
0.0b	(sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))
0.3b	(.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))

rewrite91.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`sqrt-div_binary64_1128`
46×	`add-sqr-sqrt_binary64_1133`
40×	`sqrt-prod_binary64_1127`
36×	`*-un-lft-identity_binary64_1111`
26×	`frac-sub_binary64_1120`
21×	`pow1_binary64_1172`
16×	`frac-times_binary64_1121` `add-cube-cbrt_binary64_1146`
13×	`flip-+_binary64_1085` `flip3--_binary64_1115` `flip3-+_binary64_1114` `flip--_binary64_1086`
12×	`swap-sqr_binary64_1078`
10×	`pow1/2_binary64_1191` `sqrt-pow1_binary64_1129`
9×	`add-log-exp_binary64_1150` `distribute-lft-out--_binary64_1063`
8×	`associate-r_binary64_1051` `associate-l_binary64_1052`
7×	`cancel-sign-sub-inv_binary64_1077` `difference-of-squares_binary64_1080`
6×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
5×	`pow-prod-up_binary64_1181`
4×	`associate-l/_binary64_1054` `rem-sqrt-square_binary64_1124` `unswap-sqr_binary64_1079` `associate-r/_binary64_1053`
3×	`times-frac_binary64_1117` `pow-sqr_binary64_1084` `pow-prod-down_binary64_1182`
2×	`diff-log_binary64_1203`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `rem-square-sqrt_binary64_1123` `pow-plus_binary64_1174` `associate--l+_binary64_1048` `pow2_binary64_1192` `sqrt-unprod_binary64_1131` `sqr-abs_binary64_1126` `sum-log_binary64_1202` `sub-neg_binary64_1104`

Counts

4 → 144

Calls

4 calls:

30.0ms	(.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
12.0ms	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))
11.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))
11.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))

series2.2s (17.4%)

Counts

4 → 12

Calls

4 calls:

928.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))
902.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))
194.0ms	(.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
176.0ms	(-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

simplify108.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4954	6989
1	4954	6989

prune327.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	154	6	160

Merged error: 0.0b

Counts

160 → 6

Compiler

Compiled 8121 to 4014 computations (50.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)))) 5) (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))))
0.3b	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
0.3b	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
0.6b	(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))) 5)

rewrite97.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64_1133` `cbrt-prod_binary64_1142`
33×	`sqrt-prod_binary64_1127`
31×	`unpow-prod-down_binary64_1190`
29×	`*-un-lft-identity_binary64_1111`
19×	`add-cube-cbrt_binary64_1146`
15×	`associate-l_binary64_1052` `unswap-sqr_binary64_1079`
12×	`sqrt-div_binary64_1128` `cbrt-div_binary64_1143`
11×	`associate-r_binary64_1051`
10×	`add-exp-log_binary64_1149`
6×	`frac-sub_binary64_1120` `pow1_binary64_1172`
5×	`add-cbrt-cube_binary64_1147` `difference-of-squares_binary64_1080` `sqr-pow_binary64_1083` `distribute-lft-out--_binary64_1063`
4×	`add-log-exp_binary64_1150` `associate-*r/_binary64_1053`
3×	`prod-exp_binary64_1160` `pow1/3_binary64_1193` `flip-+_binary64_1085` `pow-unpow_binary64_1188` `flip3--_binary64_1115` `flip3-+_binary64_1114` `flip--_binary64_1086`
2×	`pow-pow_binary64_1183` `pow-exp_binary64_1179` `pow-to-exp_binary64_1180`
1×	`*-commutative_binary64_1042` `pow-prod-up_binary64_1181` `cbrt-unprod_binary64_1144` `pow-plus_binary64_1174`

Counts

4 → 125

Calls

4 calls:

36.0ms	(.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)))) 5) (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))))
14.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))) 5)
13.0ms	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
12.0ms	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))

series2.6s (20.7%)

Counts

4 → 12

Calls

4 calls:

1.7s	(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))) 5)
379.0ms	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
377.0ms	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
192.0ms	(.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)))) 5) (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))))

simplify119.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4916	6268
1	4916	6268

prune330.0ms (2.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	137	6	143

Merged error: 0.0b

Counts

143 → 6

Compiler

Compiled 7515 to 4103 computations (45.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)))) 5/2)) (sqrt.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))))
0.3b	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
0.3b	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
0.4b	(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))) 5/2)

rewrite120.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`sqrt-div_binary64_1128`
32×	`cbrt-prod_binary64_1142`
31×	`sqrt-prod_binary64_1127`
28×	`cbrt-div_binary64_1143`
24×	`frac-sub_binary64_1120` `associate-l/_binary64_1054` `-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133`
16×	`frac-times_binary64_1121` `add-cube-cbrt_binary64_1146`
15×	`add-exp-log_binary64_1149`
14×	`associate-r_binary64_1051`
12×	`flip-+_binary64_1085` `flip3--_binary64_1115` `flip3-+_binary64_1114` `flip--_binary64_1086`
11×	`unpow-prod-down_binary64_1190`
9×	`add-cbrt-cube_binary64_1147`
7×	`prod-exp_binary64_1160` `pow1_binary64_1172`
4×	`difference-of-squares_binary64_1080` `add-log-exp_binary64_1150` `distribute-lft-out--_binary64_1063` `associate-*r/_binary64_1053`
3×	`cbrt-unprod_binary64_1144` `pow1/3_binary64_1193` `pow-unpow_binary64_1188`
2×	`pow-pow_binary64_1183` `pow-exp_binary64_1179` `pow-to-exp_binary64_1180`
1×	`-commutative_binary64_1042` `pow-prod-down_binary64_1182` `associate-l*_binary64_1052` `sqr-pow_binary64_1083`

Counts

4 → 120

Calls

4 calls:

50.0ms	(.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)))) 5/2)) (sqrt.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))))
14.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))) 5/2)
13.0ms	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
12.0ms	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))

series1.8s (13.9%)

Counts

4 → 12

Calls

4 calls:

781.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4)))) 5/2)
387.0ms	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
377.0ms	(cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))
208.0ms	(.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4))) (pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (.f64 a b) 4)))) 5/2)) (sqrt.f64 (cbrt.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 x y) (/.f64 (.f64 z t) 16)) (/.f64 (*.f64 a b) 4))))))

simplify138.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4969	8498
1	4969	8498

prune416.0ms (3.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	132	6	138

Merged error: 0.0b

Counts

138 → 6

Compiler

Compiled 9571 to 4866 computations (49.2% saved)

regimes315.0ms (2.5%)

Compiler: Compiled 3509 to 2796 computations (20.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	25
1	56	25

end0.0ms (0%)

sample1.4s (11.1%)

Algorithm

1×

intervals

Results

435.0ms	8000×	body	128	valid
221.0ms	4006×	body	128	invalid

Compiler

Compiled 260 to 210 computations (19.2% saved)

Details

analyze1.6s (12.7%)

sample40.0ms (0.3%)

simplify231.0ms (1.8%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite34.0ms (0.3%)

series483.0ms (3.8%)

simplify41.0ms (0.3%)

prune87.0ms (0.7%)

localize19.0ms (0.1%)

rewrite91.0ms (0.7%)

series2.2s (17.4%)

simplify108.0ms (0.9%)

prune327.0ms (2.6%)

localize22.0ms (0.2%)

rewrite97.0ms (0.8%)

series2.6s (20.7%)

simplify119.0ms (0.9%)

prune330.0ms (2.6%)

localize23.0ms (0.2%)

rewrite120.0ms (0.9%)

series1.8s (13.9%)

simplify138.0ms (1.1%)

prune416.0ms (3.3%)

regimes315.0ms (2.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (11.1%)

Profiling