Details

analyze40.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

sample37.0ms

Algorithm

intervals

Results

17.0ms	92×	body	1280	valid
4.0ms	34×	body	640	valid
3.0ms	98×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	80	invalid

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5377	9

prune5.0ms

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: 27.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
3.3b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1201` `add-log-exp_binary64_1181`
5×	`*-un-lft-identity_binary64_1216`
2×	`add-cbrt-cube_binary64_1188` `pow1_binary64_1162` `add-exp-log_binary64_1180` `add-cube-cbrt_binary64_1187` `difference-of-squares_binary64_1245`
1×	`flip3--_binary64_1215` `distribute-lft-out--_binary64_1261` `rem-exp-log_binary64_1178` `exp-prod_binary64_1170` `exp-to-pow_binary64_1156` `diff-log_binary64_1132` `sub-neg_binary64_1220` `difference-of-sqr-1_binary64_1246` `flip--_binary64_1242`

Counts

2 → 25

Calls

2 calls:

2.0ms	(exp.f64 (*.f64 a x))
4.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

series42.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp.f64 (*.f64 a x))
28.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

simplify60.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5406	374

prune95.0ms

Filtered

20 candidates to 31 candidates (-55.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	26	5	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	5	32

Merged error: 3.5b

Counts

32 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 (*.f64 a x)) 2)
0.0b	(+.f64 (exp.f64 (*.f64 a x)) 1)
0.0b	(/.f64 (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) -1) (+.f64 (exp.f64 (.f64 a x)) 1))
3.3b	(+.f64 (pow.f64 (exp.f64 (*.f64 a x)) 2) -1)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1216`
32×	`add-sqr-sqrt_binary64_1201` `times-frac_binary64_1211`
24×	`difference-of-sqr--1_binary64_1247`
20×	`add-cube-cbrt_binary64_1187`
16×	`distribute-lft-out_binary64_1260`
9×	`unpow-prod-down_binary64_1151` `add-log-exp_binary64_1181`
8×	`associate-/l*_binary64_1280`
7×	`unpow2_binary64_1159` `sqr-pow_binary64_1248`
6×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
5×	`pow1_binary64_1162`
4×	`flip-+_binary64_1241` `flip3-+_binary64_1214` `associate-/r*_binary64_1279`
3×	`pow-unpow_binary64_1149` `pow-pow_binary64_1144`
2×	`sum-log_binary64_1131` `associate-/r/_binary64_1281` `associate-/l/_binary64_1282` `+-commutative_binary64_1283`
1×	`div-exp_binary64_1169` `pow-exp_binary64_1140` `pow-to-exp_binary64_1141` `div-inv_binary64_1217` `clear-num_binary64_1219` `exp-prod_binary64_1170` `exp-to-pow_binary64_1156` `cbrt-undiv_binary64_1186` `frac-2neg_binary64_1209`

Counts

4 → 108

Calls

4 calls:

3.0ms	(pow.f64 (exp.f64 (*.f64 a x)) 2)
4.0ms	(+.f64 (exp.f64 (*.f64 a x)) 1)
13.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) -1) (+.f64 (exp.f64 (.f64 a x)) 1))
12.0ms	(+.f64 (pow.f64 (exp.f64 (*.f64 a x)) 2) -1)

series167.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow.f64 (exp.f64 (*.f64 a x)) 2)
17.0ms	(+.f64 (exp.f64 (*.f64 a x)) 1)
83.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 (.f64 a x)) 2) -1) (+.f64 (exp.f64 (.f64 a x)) 1))
42.0ms	(+.f64 (pow.f64 (exp.f64 (*.f64 a x)) 2) -1)

simplify86.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5091	2630

prune282.0ms

Filtered

76 candidates to 120 candidates (-57.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	120	5	125

Merged error: 3.4b

Counts

125 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 a x) 2)
0.0b	(+.f64 (exp.f64 (*.f64 a x)) 1)
0.0b	(/.f64 (+.f64 (exp.f64 (.f64 (.f64 a x) 2)) -1) (+.f64 (exp.f64 (*.f64 a x)) 1))
3.3b	(+.f64 (exp.f64 (.f64 (.f64 a x) 2)) -1)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_1216`
24×	`times-frac_binary64_1211`
23×	`add-sqr-sqrt_binary64_1201`
17×	`add-cube-cbrt_binary64_1187`
14×	`distribute-lft-out_binary64_1260`
12×	`difference-of-sqr--1_binary64_1247`
11×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
9×	`pow1_binary64_1162`
8×	`add-log-exp_binary64_1181`
6×	`associate-/l*_binary64_1280` `exp-lft-sqr_binary64_1173`
4×	`flip-+_binary64_1241` `flip3-+_binary64_1214` `associate-/r*_binary64_1279`
3×	`cbrt-unprod_binary64_1185` `pow-prod-down_binary64_1143` `prod-exp_binary64_1167` `associate-r_binary64_1275`
2×	`sum-log_binary64_1131` `associate-/r/_binary64_1281` `associate-/l/_binary64_1282` `+-commutative_binary64_1283`
1×	`div-exp_binary64_1169` `div-inv_binary64_1217` `clear-num_binary64_1219` `associate-l_binary64_1276` `cbrt-undiv_binary64_1186` `*-commutative_binary64_1284` `frac-2neg_binary64_1209`

Counts

4 → 94

Calls

4 calls:

5.0ms	(.f64 (.f64 a x) 2)
4.0ms	(+.f64 (exp.f64 (*.f64 a x)) 1)
10.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (.f64 a x) 2)) -1) (+.f64 (exp.f64 (*.f64 a x)) 1))
5.0ms	(+.f64 (exp.f64 (.f64 (.f64 a x) 2)) -1)

series128.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 (.f64 a x) 2)
15.0ms	(+.f64 (exp.f64 (*.f64 a x)) 1)
66.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (.f64 a x) 2)) -1) (+.f64 (exp.f64 (*.f64 a x)) 1))
33.0ms	(+.f64 (exp.f64 (.f64 (.f64 a x) 2)) -1)

simplify72.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5558	2182

prune263.0ms

Filtered

73 candidates to 106 candidates (-45.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	108	3	111

Merged error: 0.0b

Counts

111 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 a x) (+.f64 2 (.f64 (.f64 a x) 2)))
0.1b	(.f64 (pow.f64 (.f64 a x) 3) 4/3)
0.2b	(pow.f64 (*.f64 a x) 3)
13.1b	(+.f64 (.f64 (pow.f64 (.f64 a x) 3) 4/3) (.f64 (.f64 a x) (+.f64 2 (.f64 (.f64 a x) 2))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log_binary64_1180`
14×	`add-cbrt-cube_binary64_1188`
12×	`pow1_binary64_1162`
11×	`add-sqr-sqrt_binary64_1201`
9×	`-un-lft-identity_binary64_1216` `associate-l*_binary64_1276` `prod-exp_binary64_1167`
8×	`add-cube-cbrt_binary64_1187` `associate-r_binary64_1275`
6×	`add-log-exp_binary64_1181`
5×	`cbrt-unprod_binary64_1185`
4×	`pow-exp_binary64_1140` `pow-prod-down_binary64_1143`
3×	`pow-unpow_binary64_1149` `sqr-pow_binary64_1248`
2×	`unpow-prod-down_binary64_1151` `pow-to-exp_binary64_1141` `flip-+_binary64_1241` `flip3-+_binary64_1214` `unswap-sqr_binary64_1244` `associate-r/_binary64_1277` `cube-mult_binary64_1191` `associate-+r+_binary64_1267` `unpow3_binary64_1160` `-commutative_binary64_1284` `pow-pow_binary64_1144` `distribute-lft-in_binary64_1258` `cube-prod_binary64_1189` `distribute-rgt-in_binary64_1259` `rem-cube-cbrt_binary64_1192`
1×	`sum-log_binary64_1131` `distribute-rgt1-in_binary64_1265` `distribute-rgt-out_binary64_1262` `+-commutative_binary64_1283`

Counts

4 → 85

Calls

4 calls:

7.0ms	(.f64 (.f64 a x) (+.f64 2 (.f64 (.f64 a x) 2)))
6.0ms	(.f64 (pow.f64 (.f64 a x) 3) 4/3)
4.0ms	(pow.f64 (*.f64 a x) 3)
7.0ms	(+.f64 (.f64 (pow.f64 (.f64 a x) 3) 4/3) (.f64 (.f64 a x) (+.f64 2 (.f64 (.f64 a x) 2))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(.f64 (.f64 a x) (+.f64 2 (.f64 (.f64 a x) 2)))
54.0ms	(.f64 (pow.f64 (.f64 a x) 3) 4/3)
36.0ms	(pow.f64 (*.f64 a x) 3)
88.0ms	(+.f64 (.f64 (pow.f64 (.f64 a x) 3) 4/3) (.f64 (.f64 a x) (+.f64 2 (.f64 (.f64 a x) 2))))

simplify53.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5735	1520

prune272.0ms

Filtered

62 candidates to 97 candidates (-56.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	97	3	100

Merged error: 0b

Counts

100 → 3

regimes243.0ms

Accuracy

97.1% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 21.1b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	105
1	42	105

end0.0ms

sample988.0ms

Algorithm

intervals

Results

481.0ms	2715×	body	1280	valid
154.0ms	1315×	body	640	valid
77.0ms	2774×	body	80	valid
59.0ms	751×	body	320	valid
26.0ms	445×	body	160	valid
4.0ms	137×	body	80	invalid

Details

analyze40.0ms

sample37.0ms

simplify79.0ms

prune5.0ms

localize7.0ms

rewrite6.0ms

series42.0ms

simplify60.0ms

prune95.0ms

localize13.0ms

rewrite36.0ms

series167.0ms

simplify86.0ms

prune282.0ms

localize14.0ms

rewrite27.0ms

series128.0ms

simplify72.0ms

prune263.0ms

localize21.0ms

rewrite26.0ms

series224.0ms

simplify53.0ms

prune272.0ms

regimes243.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample988.0ms

Profiling