Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	234×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	9×	body	1280	valid
0.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	109	6
3	195	6
4	445	6
5	828	6
6	1434	6
7	2520	6
8	4830	6
9	5001	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 17.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.1b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.5b	(/ (* (- z t) y) (- a t))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-l` `associate-/r*` `distribute-lft-out--`
4×	`flip3--` `associate-*l/` `flip--` `difference-of-squares`
3×	`associate-r`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 70

Calls

3 calls:

6.0ms	(* (- z t) y)
10.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms	(/ (* (- z t) y) (- a t))

series200.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* (- z t) y)
110.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
63.0ms	(/ (* (- z t) y) (- a t))

simplify46.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	383	461
1	1704	422
2	5001	422

prune188.0ms

Filtered

79 candidates to 56 candidates (70.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	11	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	11	80

Merged error: 4.7b

Counts

80 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.0b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.2b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `frac-times` `div-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 127

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
31.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (- a t))
142.0ms	(cbrt (- a t))
95.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
110.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	785	1736
1	3321	1577
2	5002	1498

prune394.0ms

Filtered

139 candidates to 104 candidates (74.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	139	11	150

Merged error: 4.6b

Counts

150 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

6.3b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
6.3b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
6.3b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
9.1b	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

297×	`cbrt-div`
261×	`frac-times`
153×	`associate-*l/`
129×	`associate-*r/`
126×	`frac-sub`
63×	`flip3-+` `flip-+`
9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 176

Calls

4 calls:

18.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
18.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
19.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
19.0ms	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
285.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
291.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
176.0ms	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))

simplify221.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	1756	9997
1	4189	9460
2	5001	9279

prune523.0ms

Filtered

188 candidates to 95 candidates (50.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	187	12	199

Merged error: 4.6b

Counts

199 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.3b	(- (+ x y) (* (- z t) (/ y (- a t))))
10.2b	(* (- z t) (/ y (- a t)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-exp-log` `frac-sub` `add-cbrt-cube`
9×	`flip3--` `flip--`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`frac-times` `associate-*l/`
5×	`pow1` `flip3-+` `associate-l` `associate-/r*` `flip-+`
4×	`associate-/r/`
3×	`associate-r/` `associate-/l`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `*-commutative`

Counts

3 → 107

Calls

3 calls:

5.0ms	(/ y (- a t))
6.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
16.0ms	(* (- z t) (/ y (- a t)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ y (- a t))
117.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
60.0ms	(* (- z t) (/ y (- a t)))

simplify66.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	559	844
1	2676	803
2	5001	803

prune245.0ms

Filtered

116 candidates to 83 candidates (71.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	113	15	128

Merged error: 4.6b

Counts

128 → 15

regimes392.0ms

Accuracy

28.6% (5.8b remaining)

Error of 9.5b against oracle of 3.7b and baseline of 11.9b

bsearch84.0ms

Steps

Iters	Range		Point
7	3.1953327204785303e-102	7.541288183187102e-101	2.1385292439727694e-101
8	-2.0156036062966428e-138	-8.169466393489241e-143	-1.0133500180639392e-138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample759.0ms

Algorithm

intervals

Results

290.0ms	7379×	body	80	valid
70.0ms	456×	body	640	valid
42.0ms	241×	body	1280	valid
39.0ms	374×	body	320	valid
22.0ms	277×	body	160	valid
4.0ms	19×	body	2560	valid