Details

sample291.0ms

Algorithm

intervals

Results

214.0ms	154×	body	1280	valid
44.0ms	59×	body	640	valid
7.0ms	14×	body	320	valid
3.0ms	20×	body	80	valid
3.0ms	9×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune6.0ms

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: 12.0b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(cos (- lambda1 lambda2))
2.5b	(sin (- lambda1 lambda2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series51.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
28.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune178.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	57	15	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	15	73

Merged error: 6.5b

Counts

73 → 15

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(cos (- lambda1 lambda2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
7.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series68.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
29.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
24.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	348	646
1	1462	557
2	5001	557

prune158.0ms

Filtered

56 candidates to 82 candidates (-46.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 0.1b

Counts

97 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 89

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
9.0ms	(* (sin lambda1) (sin lambda2))
27.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify58.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	433	949
1	2002	747
2	5001	747

prune159.0ms

Filtered

59 candidates to 101 candidates (-71.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Merged error: 0.1b

Counts

111 → 10

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
7.4b	(cbrt (* (sin lambda1) (sin lambda2)))
7.4b	(cbrt (* (sin lambda1) (sin lambda2)))
7.4b	(cbrt (* (sin lambda1) (sin lambda2)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod` `cbrt-div` `sin-mult`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

6.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
21.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
26.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
21.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify118.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	199	632
1	731	547
2	4086	514
3	5002	504

prune96.0ms

Filtered

54 candidates to 76 candidates (-40.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	76	10	86

Merged error: 0.1b

Counts

86 → 10

regimes606.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	40
1	39	40

end0.0ms

sample8.7s

Algorithm

intervals

Results

6.3s	4633×	body	1280	valid
1.5s	1940×	body	640	valid
302.0ms	572×	body	320	valid
101.0ms	651×	body	80	valid
64.0ms	204×	body	160	valid

Details

sample291.0ms

simplify8.0ms

prune6.0ms

localize26.0ms

rewrite22.0ms

series51.0ms

simplify104.0ms

prune178.0ms

localize35.0ms

rewrite23.0ms

series68.0ms

simplify45.0ms

prune158.0ms

localize35.0ms

rewrite33.0ms

series95.0ms

simplify58.0ms

prune159.0ms

localize42.0ms

rewrite18.0ms

series98.0ms

simplify118.0ms

prune96.0ms

regimes606.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.7s

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