Details

sample74.0ms

Algorithm

intervals

Results

18.0ms	240×	body	80	valid
17.0ms	15×	body	640	valid
3.0ms	16×	body	320	valid
3.0ms	8×	body	1280	valid
1.0ms	6×	body	160	valid

simplify14.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (48.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	109	13
4	203	12
5	451	12
6	748	12
7	1078	12
8	1400	12
9	1655	12
10	2153	12
11	2683	12
12	3847	12
done	5001	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.0b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

42.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series299.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- t z) (- a t))
246.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify1.4s

Counts

70 → 70

Iterations

Useful iterations: 3 (425.0ms)

Iter	Nodes	Cost
0	113	906
1	258	878
2	622	826
3	1643	824
done	5000	824

prune304.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- t z) (/ 1 (- a t)))
5.2b	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

25.0ms	(/ 1 (- a t))
101.0ms	(* (- t z) (/ 1 (- a t)))
1.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

series397.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ 1 (- a t))
77.0ms	(* (- t z) (/ 1 (- a t)))
274.0ms	(fma (* (- t z) (/ 1 (- a t))) y (+ x y))

simplify2.8s

Counts

114 → 114

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	149	1273
1	328	1040
2	908	936
3	3048	934
done	5001	934

prune390.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
8.6b	(fma (* (- t z) (* (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (/ 1 (cbrt (- a t))))) y (+ x y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
6.0ms	(cbrt (- a t))
0.0ms	(fma (* (- t z) (* (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (/ 1 (cbrt (- a t))))) y (+ x y))

series956.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(cbrt (- a t))
219.0ms	(cbrt (- a t))
209.0ms	(cbrt (- a t))
233.0ms	(fma (* (- t z) (* (/ (/ 1 (cbrt (- a t))) (cbrt (- a t))) (/ 1 (cbrt (- a t))))) y (+ x y))

simplify1.2s

Counts

73 → 73

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	95	965
1	196	947
2	432	847
3	1203	666
done	5000	630

prune420.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.6b	(+ (* y (/ (- t z) (- a t))) (+ x y))
2.3b	(* y (/ (- t z) (- a t)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `associate-/r` `associate-/l`
4×	`associate-/r/`
3×	`expm1-log1p-u` `flip3--` `associate-r/` `associate-l*` `sum-log` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3-+` `div-exp` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `fma-def` `frac-2neg` `div-sub` `pow-prod-down` `clear-num` `*-commutative`

Counts

3 → 124

Calls

3 calls:

28.0ms	(/ (- t z) (- a t))
32.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))
79.0ms	(* y (/ (- t z) (- a t)))

series417.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- t z) (- a t))
238.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))
104.0ms	(* y (/ (- t z) (- a t)))

simplify1.4s

Counts

133 → 133

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	190	1752
1	524	1625
2	1648	1541
done	5000	1530

prune520.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

regimes521.0ms

Accuracy

33.9% (5.7b remaining)

Error of 9.1b against oracle of 3.3b and baseline of 12.0b

bsearch136.0ms

Steps

Iters	Range		Point
6	1.3224209822744155e-152	2.0773317564981393e-151	1.0197674687672387e-151
9	-8.737480952231656e-149	-2.1349897266323535e-158	-9.468901046412142e-153

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	52
1	32	52
done	32	52

end0.0ms

sample1.5s

Algorithm

intervals

Results

616.0ms	7339×	body	80	valid
128.0ms	469×	body	640	valid
85.0ms	388×	body	320	valid
67.0ms	261×	body	1280	valid
27.0ms	250×	body	160	valid
5.0ms	19×	body	2560	valid